Mathematics Problems

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…

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

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 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

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 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 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 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 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 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 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 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 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  

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 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 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…

if x^x y^y z^z=c show thatn (∂^2 z)/∂x∂y=-(1+logx)(1+logy)/(z(1+logz)^3) and hence deduce that (∂^2 z)/∂x∂y=-(xlog(ex))^-1 when x=y=z Question Solution Question if x^x y^y z^z=c show thatn (∂^2 z)/∂x∂y=-(1+logx)(1+logy)/(z(1+logz)^3) and hence deduce that (∂^2 z)/∂x∂y=-(xlog(ex))^-1 when x=y=z   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…