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Mathematics & Economics
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Math Problem
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# 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

source..
Content:

Partial Differential Equation
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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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