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Mathematics & Economics

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Math Problem

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Topic:

# Solving Partial Differential Equation (Math Problem Sample)

Instructions:

1: find the general integral surface of the quasi-linear differential equation

x(y^2-z)p+y(x^2+z)=(x^2-y^2 )z

Content:

Partial Differential Equation

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Question 1 Answer

Rewrite the general integral surface of the quasi-linear differential equation

xy2-zp+yx2+z=x2-y2z

Solution

dxxy2-z=dy-yx2+z=dzx2-y2z

dxx+dyy+dzz=0y2-z-x2+z+x2-y2=0

dxx+dyy+dzz=0

dxx+dyy+dzz=c1

lnxyz=lnc1xyz=c1

Again

dxxy2-z=dy-yx2+z=dzx2-y2z

xdxx2y2-z=ydy-y2x2+z=dzx2-y2z

xdx+ydy+dz=0x2y2-zx2y2-z-x2-y2z=0

xdx+ydy+dz=0

xdx+ydy-dz=c2

x2+y2-2z=c2

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