Solve rsinθ-cosθdr/dθ=r^2
Solve rsinθ-cosθdr/dθ=r^2 Question Solution Problem Solve rsinθ-cosθdr/dθ=r^2 Related Questions Solve dy/dx+ytanx = y^2 secx Solve rsinθ-cosθdr/dθ=r^2 Solve x^3 dy/dx - x^2 y = -y^2 cosx Solve xy(1+xy^2)dy/dx=1
Solve dy/dx+ytanx = y^2 secx
Solve dy/dx+ytanx = y^2 secx Question Solution Problem Solve dy/dx+ytanx = y^2 secx Related Questions Solve dy/dx+ytanx = y^2 secx Solve rsinθ-cosθdr/dθ=r^2 Solve x^3 dy/dx - x^2 y = -y^2 cosx Solve xy(1+xy^2)dy/dx=1
Exact differential equations
Exact Differential Equations An exact differential equation is a type of ordinary differential equation (ODE) in which the total differential of a function is equal to the product of a function and a differential. Exact differential equations have the property that their solutions are unique, provided suitable initial or boundary conditions are specified. TYPE 1 For any given function f(x,y), the necessary and the sufficient condition for the differential equations M (x,y)dx+N(x,y)dy=0 to be an exact equation is Type 2…
Solve (2xlogx–xy)dy + 2ydx = 0
Solve (2xlogx–xy)dy + 2ydx = 0 Question Solve (2xlogx–xy)dy + 2ydx = 0 Solution Problem Solve (2xlogx–xy)dy + 2ydx = 0 Topic Exact differential equations Type 1 Questions Solve dy/dx+(x+3y-4)/(3x+9y-2)=0 Solve dy/dx+(y cosx +siny +y)/(sinx + xcosy +x)=0 Solve ye^xy dx+(xe^xy +2y)dy=0 Solve (1+e^(x/y))dx+e^(x/y) (1-x/y)dy=0 Solve (y^2 e^(xy^2) + 4x^3)dx+(2xy e^(xy^2)-3y^2)dy=0 Solve 2x/y^3 dx+(y^2-3x^2/y^4) dy=0 Type 2 Questions Solve (4xy+3y^2–x)dx+x(x+2y)dy=0 Solve (x^2+y^2+x)dx+xydy=0 Solve y(2xy+1)dx–xdy=0 Solve (2xlogx–xy)dy + 2ydx = 0
Solve y(2xy+1)dx–xdy=0
Solve y(2xy+1)dx–xdy=0 Problem Solve y(2xy+1)dx–xdy=0 Solution Problem Solve y(2xy+1)dx–xdy=0 Topic Exact differential equations Type 1 Questions Solve dy/dx+(x+3y-4)/(3x+9y-2)=0 Solve dy/dx+(y cosx +siny +y)/(sinx + xcosy +x)=0 Solve ye^xy dx+(xe^xy +2y)dy=0 Solve (1+e^(x/y))dx+e^(x/y) (1-x/y)dy=0 Solve (y^2 e^(xy^2) + 4x^3)dx+(2xy e^(xy^2)-3y^2)dy=0 Solve 2x/y^3 dx+(y^2-3x^2/y^4) dy=0 Type 2 Questions Solve (4xy+3y^2–x)dx+x(x+2y)dy=0 Solve (x^2+y^2+x)dx+xydy=0 Solve y(2xy+1)dx–xdy=0 Solve (2xlogx–xy)dy + 2ydx = 0
Solve (x^2+y^2+x)dx+xydy=0
Solve (x^2+y^2+x)dx+xydy=0 Problem Solution Problem Solve (x^2+y^2+x)dx+xydy=0 Topic Exact differential equations Type 1 Questions Solve dy/dx+(x+3y-4)/(3x+9y-2)=0 Solve dy/dx+(y cosx +siny +y)/(sinx + xcosy +x)=0 Solve ye^xy dx+(xe^xy +2y)dy=0 Solve (1+e^(x/y))dx+e^(x/y) (1-x/y)dy=0 Solve (y^2 e^(xy^2) + 4x^3)dx+(2xy e^(xy^2)-3y^2)dy=0 Solve 2x/y^3 dx+(y^2-3x^2/y^4) dy=0 Type 2 Questions Solve (4xy+3y^2–x)dx+x(x+2y)dy=0 Solve (x^2+y^2+x)dx+xydy=0 Solve y(2xy+1)dx–xdy=0 Solve (2xlogx–xy)dy + 2ydx = 0
Solve (4xy+3y^2–x)dx+x(x+2y)dy=0
Solve (4xy+3y^2–x)dx+x(x+2y)dy=0 Problem Solution Problem Solve (4xy+3y^2–x)dx+x(x+2y)dy=0 Topic Exact differential equations Type 1 Questions Solve dy/dx+(x+3y-4)/(3x+9y-2)=0 Solve dy/dx+(y cosx +siny +y)/(sinx + xcosy +x)=0 Solve ye^xy dx+(xe^xy +2y)dy=0 Solve (1+e^(x/y))dx+e^(x/y) (1-x/y)dy=0 Solve (y^2 e^(xy^2) + 4x^3)dx+(2xy e^(xy^2)-3y^2)dy=0 Solve 2x/y^3 dx+(y^2-3x^2/y^4) dy=0 Type 2 Questions Solve (4xy+3y^2–x)dx+x(x+2y)dy=0 Solve (x^2+y^2+x)dx+xydy=0 Solve y(2xy+1)dx–xdy=0 Solve (2xlogx–xy)dy + 2ydx = 0
Solve (y^2 e^(xy^2) + 4x^3)dx+(2xy e^(xy^2)-3y^2)dy=0
Solve (y^2 e^(xy^2) + 4x^3)dx+(2xy e^(xy^2)-3y^2)dy=0 Problem Solution Problem Solve (y^2 e^(xy^2) + 4x^3)dx+(2xy e^(xy^2)-3y^2)dy=0 Topic Exact differential equations Type 1 Questions Solve dy/dx+(x+3y-4)/(3x+9y-2)=0 Solve dy/dx+(y cosx +siny +y)/(sinx + xcosy +x)=0 Solve ye^xy dx+(xe^xy +2y)dy=0 Solve (1+e^(x/y))dx+e^(x/y) (1-x/y)dy=0 Solve (y^2 e^(xy^2) + 4x^3)dx+(2xy e^(xy^2)-3y^2)dy=0 Solve 2x/y^3 dx+(y^2-3x^2/y^4) dy=0 Type 2 Questions Solve (4xy+3y^2–x)dx+x(x+2y)dy=0 Solve (x^2+y^2+x)dx+xydy=0 Solve y(2xy+1)dx–xdy=0 Solve (2xlogx–xy)dy + 2ydx = 0
Solve (1+e^(x/y))dx+e^(x/y) (1-x/y)dy=0
Solve (1+e^(x/y))dx+e^(x/y) (1-x/y)dy=0 Problem Solution Problem Solve (1+e^(x/y))dx+e^(x/y) (1-x/y)dy=0 Topic Exact differential equations Type 1 Questions Solve dy/dx+(x+3y-4)/(3x+9y-2)=0 Solve dy/dx+(y cosx +siny +y)/(sinx + xcosy +x)=0 Solve ye^xy dx+(xe^xy +2y)dy=0 Solve (1+e^(x/y))dx+e^(x/y) (1-x/y)dy=0 Solve (y^2 e^(xy^2) + 4x^3)dx+(2xy e^(xy^2)-3y^2)dy=0 Solve 2x/y^3 dx+(y^2-3x^2/y^4) dy=0 Type 2 Questions Solve (4xy+3y^2–x)dx+x(x+2y)dy=0 Solve (x^2+y^2+x)dx+xydy=0 Solve y(2xy+1)dx–xdy=0 Solve (2xlogx–xy)dy + 2ydx = 0
Solve ye^xy dx+(xe^xy +2y)dy=0
Solve ye^xy dx+(xe^xy +2y)dy=0 Problem Solution Problem Solve ye^xy dx+(xe^xy +2y)dy=0 Topic Exact differential equations Type 1 Questions Solve dy/dx+(x+3y-4)/(3x+9y-2)=0 Solve dy/dx+(y cosx +siny +y)/(sinx + xcosy +x)=0 Solve ye^xy dx+(xe^xy +2y)dy=0 Solve (1+e^(x/y))dx+e^(x/y) (1-x/y)dy=0 Solve (y^2 e^(xy^2) + 4x^3)dx+(2xy e^(xy^2)-3y^2)dy=0 Solve 2x/y^3 dx+(y^2-3x^2/y^4) dy=0 Type 2 Questions Solve (4xy+3y^2–x)dx+x(x+2y)dy=0 Solve (x^2+y^2+x)dx+xydy=0 Solve y(2xy+1)dx–xdy=0 Solve (2xlogx–xy)dy + 2ydx = 0
Solve dy/dx+(y cosx +siny +y)/(sinx + xcosy +x)=0
Solve dy/dx+(y cosx +siny +y)/(sinx + xcosy +x)=0 Problem Solution Problem Solve dy/dx+(y cosx +siny +y)/(sinx + xcosy +x)=0 Topic Exact differential equations Type 1 Questions Solve dy/dx+(x+3y-4)/(3x+9y-2)=0 Solve dy/dx+(y cosx +siny +y)/(sinx + xcosy +x)=0 Solve ye^xy dx+(xe^xy +2y)dy=0 Solve (1+e^(x/y))dx+e^(x/y) (1-x/y)dy=0 Solve (y^2 e^(xy^2) + 4x^3)dx+(2xy e^(xy^2)-3y^2)dy=0 Solve 2x/y^3 dx+(y^2-3x^2/y^4) dy=0 Type 2 Questions Solve (4xy+3y^2–x)dx+x(x+2y)dy=0 Solve (x^2+y^2+x)dx+xydy=0 Solve y(2xy+1)dx–xdy=0 Solve (2xlogx–xy)dy + 2ydx = 0
Solve dy/dx+(x+3y-4)/(3x+9y-2)=0
Solve dy/dx+(x+3y-4)/(3x+9y-2)=0 Problem Solution Problem Solve dy/dx+(x+3y-4)/(3x+9y-2)=0 Topic Exact differential equations Type 1 Questions Solve dy/dx+(x+3y-4)/(3x+9y-2)=0 Solve dy/dx+(y cosx +siny +y)/(sinx + xcosy +x)=0 Solve ye^xy dx+(xe^xy +2y)dy=0 Solve (1+e^(x/y))dx+e^(x/y) (1-x/y)dy=0 Solve (y^2 e^(xy^2) + 4x^3)dx+(2xy e^(xy^2)-3y^2)dy=0 Solve 2x/y^3 dx+(y^2-3x^2/y^4) dy=0 Type 2 Questions Solve (4xy+3y^2–x)dx+x(x+2y)dy=0 Solve (x^2+y^2+x)dx+xydy=0 Solve y(2xy+1)dx–xdy=0 Solve (2xlogx–xy)dy + 2ydx = 0
How to Use Default Parameter Values in Java
In this blog post, we will learn how to use default parameter values in Java. Java has many ways to define default values for parameters in methods. This can help reduce the amount of code we write, and make our code more readable and easier to maintain. What are Default Parameter Values? A default parameter value is a value assigned to a parameter in a method if no value is provided by the calling code. It's a useful feature when…
Generating Random Alpha-Numeric Strings in Java
Random alpha-numeric strings are used in a variety of applications, from generating unique IDs and passwords to creating temporary activation codes and more. In this guide, we will show you how to generate random alpha-numeric strings in Java. Why Use Random Alpha-Numeric Strings Random alpha-numeric strings are important in software development because they provide a way to create unique identifiers that can be used for a variety of purposes. For example, you may need to generate a unique user ID…
JUnit: How to Confirm Exceptions with Assertions
JUnit is a popular Java-based testing framework for writing and running tests for applications. In JUnit, you can write tests to ensure that your code behaves as expected, including verifying that exceptions are thrown in the correct circumstances. In this post, we'll cover how to use assertions to confirm that exceptions are thrown in your JUnit tests. Understanding JUnit Assertions Before diving into how to assert exceptions, let's first understand what assertions are in JUnit. In JUnit, an assertion is…
How to Create an Executable JAR with Maven and Dependencies
In this post, we'll learn how to create an executable JAR file that contains all the dependencies required to run a Java application using Maven. Maven is a popular build tool that can simplify the process of creating JAR files with dependencies. What is an executable JAR? An executable JAR is a standard Java archive file that can be run directly without the need to extract its contents. It contains the compiled classes, resources, and dependencies of a Java application,…
Why is Processing a Sorted Array Faster than Processing an Unsorted Array in Java
Sorting arrays before processing them in Java can lead to significant performance improvements in certain situations. This is because sorting an array allows for more efficient processing techniques, such as binary search, to be used. In this post, we will discuss why processing a sorted array is faster than processing an unsorted array in Java. Binary Search One of the main reasons why processing a sorted array is faster in Java is due to the ability to use binary search.…
if u=f(r), where r=√(x^2+y^2+z^2), then show that ((∂^2 u)/(∂x^2))+((∂^2 u)/(∂y^2))+((∂^2 u)/(∂z^2))=f”(r)+(2/r)f'(r)
if u=f(r), where r=√(x^2+y^2+z^2), then show that ((∂^2 u)/(∂x^2))+((∂^2 u)/(∂y^2))+((∂^2 u)/(∂z^2))=f''(r)+(2/r)f'(r) Question Solution Question if u=f(r), where r=√(x^2+y^2+z^2), then show that ((∂^2 u)/(∂x^2))+((∂^2 u)/(∂y^2))+((∂^2 u)/(∂z^2))=f''(r)+(2/r)f'(r) Type 1 Questions if u=x^3-3xy^2+x+(e^x cosy)+1, show that ((∂^2 u)/(∂x^2))+((∂^2 u)/(∂y^2))=0 if u= log((x^2+y^2)/(x+y)), show that xu_x+yu_y=1 if u=tan^(-1)(y/x), verify that (∂^2 u)/(∂y ∂x) = (∂^2 u)/(∂x ∂y) if u=e^(ax+by)f(ax-by), prove that (b ∂u/∂x)+(a ∂u/∂y)=2abu if u=1/√(x^2+y^2+z^2), then show that ((∂^2 u)/(∂x^2))+((∂^2 u)/(∂y^2))+((∂^2 u)/(∂z^2))=0 if u=log√(x^2+y^2+z^2), then show that (x^2+y^2+z^2)(((∂^2 u)/(∂x^2))+((∂^2 u)/(∂y^2))+((∂^2 u)/(∂z^2)))=1 …
if r^2=(x-a)^2+(y-b)^2+(z-c)^2, show that ((∂^2 r)/(∂x^2))+((∂^2 r)/∂y^2))+((∂^2 r)/∂z^2))=2/r
if r^2=(x-a)^2+(y-b)^2+(z-c)^2, show that ((∂^2 r)/(∂x^2))+((∂^2 r)/∂y^2))+((∂^2 r)/∂z^2))=2/r Question Solution Question if r^2=(x-a)^2+(y-b)^2+(z-c)^2, show that ((∂^2 r)/(∂x^2))+((∂^2 r)/∂y^2))+((∂^2 r)/∂z^2))=2/r Type 1 Questions if u=x^3-3xy^2+x+(e^x cosy)+1, show that ((∂^2 u)/(∂x^2))+((∂^2 u)/(∂y^2))=0 if u= log((x^2+y^2)/(x+y)), show that xu_x+yu_y=1 if u=tan^(-1)(y/x), verify that (∂^2 u)/(∂y ∂x) = (∂^2 u)/(∂x ∂y) if u=e^(ax+by)f(ax-by), prove that (b ∂u/∂x)+(a ∂u/∂y)=2abu if u=1/√(x^2+y^2+z^2), then show that ((∂^2 u)/(∂x^2))+((∂^2 u)/(∂y^2))+((∂^2 u)/(∂z^2))=0 if u=log√(x^2+y^2+z^2), then show that (x^2+y^2+z^2)(((∂^2 u)/(∂x^2))+((∂^2 u)/(∂y^2))+((∂^2 u)/(∂z^2)))=1 Type 2 Questions if x^x y^y…
if x=rcosθ and y=rsinθ, prove that ((∂^2 r)/(∂x^2))+((∂^2 r)/∂y^2))=1/r [(∂r/∂x)^2+(∂r/∂y)^2] and ∂r/∂x=∂x/∂r
if x=rcosθ and y=rsinθ, prove that ((∂^2 r)/(∂x^2))+((∂^2 r)/∂y^2))=1/r [(∂r/∂x)^2+(∂r/∂y)^2] and ∂r/∂x=∂x/∂r Question Solution Question if x=rcosθ and y=rsinθ, prove that ((∂^2 r)/(∂x^2))+((∂^2 r)/∂y^2))=1/r [(∂r/∂x)^2+(∂r/∂y)^2] and ∂r/∂x=∂x/∂r Type 1 Questions if u=x^3-3xy^2+x+(e^x cosy)+1, show that ((∂^2 u)/(∂x^2))+((∂^2 u)/(∂y^2))=0 if u= log((x^2+y^2)/(x+y)), show that xu_x+yu_y=1 if u=tan^(-1)(y/x), verify that (∂^2 u)/(∂y ∂x) = (∂^2 u)/(∂x ∂y) if u=e^(ax+by)f(ax-by), prove that (b ∂u/∂x)+(a ∂u/∂y)=2abu if u=1/√(x^2+y^2+z^2), then show that ((∂^2 u)/(∂x^2))+((∂^2 u)/(∂y^2))+((∂^2 u)/(∂z^2))=0 if u=log√(x^2+y^2+z^2), then show that (x^2+y^2+z^2)(((∂^2 u)/(∂x^2))+((∂^2 u)/(∂y^2))+((∂^2…
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