If z = sin (ax+y) + cos (ax-y), Prove that (del)^2 z / del x^2 = a^2 (del)^2 z / del y^2 Question Question If z = sin (ax+y) + cos (ax-y), Prove that (del)^2 z / del x^2 = a^2 (del)^2 z / del y^2 Total Derivatives Problems Find du/dt when u=x^3 y^2+x^2 y^3 with x=at^2, y=2at. Use partial derivatives. Find du/dt if u=xy+yz+zx and x=t cost , y=tsint , z=t @ t=π/4 If u=f(x/y, y/z, z/x) prove that…
If z=f(x, y) where x=r cos(theta) and y=r sin(theta), Show that (del z/del x)^2 + (del z/del y) ^2 = (del z/del r)^2+1/r^2 . (del z/del (theta))^2 Question Question If z=f(x, y) where x=r cos(theta) and y=r sin(theta), Show that (del z/del x)^2 + (del z/del y) ^2 = (del z/del r)^2+1/r^2 . (del z/del (theta))^2 Total Derivatives Problems Find du/dt when u=x^3 y^2+x^2 y^3 with x=at^2, y=2at. Use partial derivatives. Find du/dt if u=xy+yz+zx and x=t cost , y=tsint…
If u=f(x-y, y-z, z-x), Show that del u/del x+del u/del y+del u/del z=0 Question Question If u=f(x-y, y-z, z-x), Show that del u/del x+del u/del y+del u/del z=0 Total Derivatives Problems Find du/dt when u=x^3 y^2+x^2 y^3 with x=at^2, y=2at. Use partial derivatives. Find du/dt if u=xy+yz+zx and x=t cost , y=tsint , z=t @ t=π/4 If u=f(x/y, y/z, z/x) prove that p=x/y, q=y/z, r=z/x If u=f(x-y, y-z, z-x), Show that del u/del x+del u/del y+del u/del z=0 If z=f(x,…
If u=f(x/y, y/z, z/x) prove that p=x/y, q=y/z, r=z/x Question Question If u=f(x/y, y/z, z/x) prove that p=x/y, q=y/z, r=z/x Total Derivatives Problems Find du/dt when u=x^3 y^2+x^2 y^3 with x=at^2, y=2at. Use partial derivatives. Find du/dt if u=xy+yz+zx and x=t cost , y=tsint , z=t @ t=π/4 If u=f(x/y, y/z, z/x) prove that p=x/y, q=y/z, r=z/x If u=f(x-y, y-z, z-x), Show that del u/del x+del u/del y+del u/del z=0 If z=f(x, y) where x=r cos(theta) and y=r sin(theta), Show…
Find du/dt if u=xy+yz+zx and x=t cost , y=tsint , z=t @ t=π/4 Question Question Find du/dt if u=xy+yz+zx and x=t cost , y=tsint , z=t @ t=π/4 Total Derivatives Problems Find du/dt when u=x^3 y^2+x^2 y^3 with x=at^2, y=2at. Use partial derivatives. Find du/dt if u=xy+yz+zx and x=t cost , y=tsint , z=t @ t=π/4 If u=f(x/y, y/z, z/x) prove that p=x/y, q=y/z, r=z/x If u=f(x-y, y-z, z-x), Show that del u/del x+del u/del y+del u/del z=0 If z=f(x,…
Find du/dt when u=x^3 y^2+x^2 y^3 with x=at^2, y=2at. Use partial derivatives Question Question Find du/dt when u=x^3 y^2+x^2 y^3 with x=at^2, y=2at. Use partial derivatives Total Derivatives Problems Find du/dt when u=x^3 y^2+x^2 y^3 with x=at^2, y=2at. Use partial derivatives. Find du/dt if u=xy+yz+zx and x=t cost , y=tsint , z=t @ t=π/4 If u=f(x/y, y/z, z/x) prove that p=x/y, q=y/z, r=z/x If u=f(x-y, y-z, z-x), Show that del u/del x+del u/del y+del u/del z=0 If z=f(x, y) where…
Differentiation of composite functions If u=f(x_1 y)then total differential equation of 'u' is given by Type 1 : Total derivative rule If u=f(x,y) where x=x(t) and y=y(t),then Type 2 : Total derivative Chain rule If u=f(x,y) where x=x(r,s) and y=y(r,s),then u is a function of (x,y),x and y are dependant on (r,s),hence u becomes a function depndant on (r,s) Total Derivatives Problems Find du/dt when u=x^3 y^2+x^2 y^3 with x=at^2, y=2at. Use partial derivatives. Find du/dt if u=xy+yz+zx and x=t…
If v(x,y))=(1-2xy+y^2)^(-1/2) and x del v/del x-y del v/del y=y^2 v^k, then find k. If v(x,y))=(1-2xy+y^2)^(-1/2) and x ∂v/∂x-y ∂v/∂y=y^2 v^k,then find k. Question Question If v(x,y))=(1-2xy+y^2)^(-1/2) and x del v/del x-y del v/del y=y^2 v^k, then find k. If v(x,y))=(1-2xy+y^2)^(-1/2) and x ∂v/∂x-y ∂v/∂y=y^2 v^k,then find k. Euler’s theorem Problems If u=(x^3+y^3)/sqrt(x+y) prove that x du/dx + y du/dy = 5/2 uIf u=(x^3+y^3)/sqrt(x+y) prove that x del u/del x + y del u/del y = 5/2 uprove that x…
If u=sin^(-1)((x+2y+3z)/(x^8+y^8+z^8)) then find x del u/del x+y del u/del y+z del u/del z If u=sin^(-1)((x+2y+3z)/(x^8+y^8+z^8)) then find x ∂u/∂x+y ∂u/∂y+z ∂u/∂z Question Question If u=sin^(-1)((x+2y+3z)/(x^8+y^8+z^8)) then find x del u/del x+y del u/del y+z del u/del z If u=sin^(-1)((x+2y+3z)/(x^8+y^8+z^8)) then find x ∂u/∂x+y ∂u/∂y+z ∂u/∂z Euler’s theorem Problems If u=(x^3+y^3)/sqrt(x+y) prove that x du/dx + y du/dy = 5/2 uIf u=(x^3+y^3)/sqrt(x+y) prove that x del u/del x + y del u/del y = 5/2 uprove that x ∂u/∂x+y ∂u/∂y=5/2…
State Euler’s theorem and use it to find, x del u/del x+y del u/del y when u=tan^(-1) ((x^2+y^2)/(x+y)) State Euler's theorem and use it to find, x∂u/∂x+y∂u/∂y when u=tan^(-1)((x^2+y^2)/(x+y)) Question Question State Euler’s theorem and use it to find, x del u/del x+y del u/del y when u=tan^(-1) ((x^2+y^2)/(x+y)) State Euler's theorem and use it to find, x∂u/∂x+y∂u/∂y when u=tan^(-1)((x^2+y^2)/(x+y)) Euler’s theorem Problems If u=(x^3+y^3)/sqrt(x+y) prove that x du/dx + y du/dy = 5/2 uIf u=(x^3+y^3)/sqrt(x+y) prove that x del…
If u=cosec^(-1) ((x^(1/2)+y^(1/2))/(x^(1/3) +y^(1/3) )), Show that x.del u/del x+y.del u/del y=(-1)/6.tan u If u=cosec^(-1) ((x^(1/2)+y^(1/2))/(x^(1/3)+y^(1/3) )),Show that x.∂u/∂x+y.∂u/∂y=(-1)/6 tanu Question Question If u=cosec^(-1) ((x^(1/2)+y^(1/2))/(x^(1/3) +y^(1/3) )), Show that x.del u/del x+y.del u/del y=(-1)/6.tan u If u=cosec^(-1) ((x^(1/2)+y^(1/2))/(x^(1/3)+y^(1/3) )),Show that x.∂u/∂x+y.∂u/∂y=(-1)/6 tanu Euler’s theorem Problems If u=(x^3+y^3)/sqrt(x+y) prove that x du/dx + y du/dy = 5/2 uIf u=(x^3+y^3)/sqrt(x+y) prove that x del u/del x + y del u/del y = 5/2 uprove that x ∂u/∂x+y ∂u/∂y=5/2 u If u=√(x^4+y^4) tan^-1(y/x),…
if u=sin^(-1)((x^2+y^2)/(x+y)), Show that x del u/del x+y del u/del y=tan u If u=sin^(-1)((x^2+y^2)/(x+y)), Show that x ∂u/∂x+y ∂u/∂y=tan u Question Question if u=sin^(-1)((x^2+y^2)/(x+y)), Show that x del u/del x+y del u/del y=tan u If u=sin^(-1)((x^2+y^2)/(x+y)), Show that x ∂u/∂x+y ∂u/∂y=tan u Euler’s theorem Problems If u=(x^3+y^3)/sqrt(x+y) prove that x du/dx + y du/dy = 5/2 uIf u=(x^3+y^3)/sqrt(x+y) prove that x del u/del x + y del u/del y = 5/2 uprove that x ∂u/∂x+y ∂u/∂y=5/2 u If u=√(x^4+y^4) tan^-1(y/x),…
If u=tan^(-1)((x^3+y^3)/(x+y)), Show that 1. x u_x+y u_y = sin2u 2. x^2 u_xx+2x_y u_xy+y^2 u_yy=sin4u-sin2u If u=tan^(-1)((x^3+y^3)/(x+y)), Show that 1.xu_x+yu_y=sin2u 2.x^2 u_xx+2x_y u_xy+y^2 u_yy=sin4u-sin2u using Euler’s theorem Question Question If u=tan^(-1)((x^3+y^3)/(x+y)), Show that 1. x u_x+y u_y = sin2u 2. x^2 u_xx+2x_y u_xy+y^2 u_yy=sin4u-sin2u If u=tan^(-1)((x^3+y^3)/(x+y)), Show that 1.xu_x+yu_y=sin2u 2.x^2 u_xx+2x_y u_xy+y^2 u_yy=sin4u-sin2u Euler’s theorem Problems If u=(x^3+y^3)/sqrt(x+y) prove that x du/dx + y du/dy = 5/2 uIf u=(x^3+y^3)/sqrt(x+y) prove that x del u/del x + y del u/del y…
If u=log((x^4+y^4)/(x+y)) Show that x del u/ del x+y del u/ del y = 3 If u=log((x^4+y^4)/(x+y)), Show that x ∂u/∂x+y ∂u/∂y=3 using Euler’s theorem Question Question If u=log((x^4+y^4)/(x+y)) Show that x del u/ del x+y del u/ del y = 3 If u=log((x^4+y^4)/(x+y)), Show that x ∂u/∂x+y ∂u/∂y=3 using Euler’s theorem Euler’s theorem Problems If u=(x^3+y^3)/sqrt(x+y) prove that x du/dx + y du/dy = 5/2 uIf u=(x^3+y^3)/sqrt(x+y) prove that x del u/del x + y del u/del y…
If u=√(x^4+y^4) tan^-1(y/x), Show that x u_x+y u_y=2u=x^2 u_xx+2xy u_xy+y^2 u_yy If u=√(x^4+y^4) tan^(-1)(y/x) Show that xu_x+yu_y=2u=x^2 u_xx+2xy uxy+y^2 u_yy Question Question If u=√(x^4+y^4) tan^-1(y/x), Show that x u_x+y u_y=2u=x^2 u_xx+2xy u_xy+y^2 u_yy If u=√(x^4+y^4) tan^(-1)(y/x) Show that xu_x+yu_y=2u=x^2 u_xx+2xy uxy+y^2 u_yy
If u=(x^3+y^3)/sqrt(x+y) prove that x du/dx + y du/dy = 5/2 u If u=(x^3+y^3)/sqrt(x+y) prove that x del u/del x + y del u/del y = 5/2 u prove that x ∂u/∂x+y ∂u/∂y=5/2 u Question Question If u=(x^3+y^3)/sqrt(x+y) prove that x du/dx + y du/dy = 5/2 u If u=(x^3+y^3)/sqrt(x+y) prove that x del u/del x + y del u/del y = 5/2 u prove that x ∂u/∂x+y ∂u/∂y=5/2 u Euler’s theorem Problems If u=(x^3+y^3)/sqrt(x+y) prove that x du/dx…
Homogenous function A function u=f(x,y) is said to be homogenous function of degree ‘n’ if it can be expressed in the form x^n g(y/x) or y^n g(x/y), ‘g’ being any arbitrary function. Similarly a function u=f(x,y,z)is said to be a homogenous function of degree ‘n’ if it can be expressed in the form Euler’s theorem on homogenous function Statement: If is a homogenous function of degree ‘n’ then Proof : Euler’s theorem Problems If u=(x^3+y^3)/sqrt(x+y) prove that x du/dx…
Standard form of a linear equation and its solution A differential equation is said to be linear if the dependent variable and its derivative occurs in the first degree only and they are not multiplied together. A differential equation of the form Bernoulli’s differential equation The Differential equation of the form Where ‘P’ and ‘Q’ are functions of ‘x’ is called Bernoulli’s differential equation in ‘y’, then divide the entire equation by and then by using variable substitution method convert…
Solve xy(1+xy^2)dy/dx=1 Question Solution Question Solve xy(1+xy^2)dy/dx=1 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 x^3 dy/dx - x^2 y = -y^2 cosx Question Solution Problem Solve x^3 dy/dx - x^2 y = -y^2 cosx 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