Question

Find the general integral of the equation: px(z-2y^2)=(z-qy)(z-y^2-2x^3)

Answer 1

Answer:

p=∂z∂x and q=∂z∂y

Find the general integral of the linear PDE px(z−2y2)=(z−qy)(z−y2−2x3).

My attempt to solve this is as follows: p=∂z∂x and q=∂z∂y

px(z−2y2)+qy(z−y2−2x3)=z(z−y2−2x3)

The Lagrange's auxiliary equation is:dxx(z−2y2)=dyy(z−y2−2x3)=dzz(z−y2−2x3)

Now consider the 2nd and 3rd ratios,

dyy(z−y2−2x3)⟹dyy⟹ln(y)⟹yz=dzz(z−y2−2x3)=dzz=ln(z)+ln(c1)=c1.

Step-by-step explanation: