Question

Let, \( p = {\partial z \over \partial x} \) and \( q = {\partial z \over \partial y}\)
Find the solution:-
\[ 1) {y^2zp \over x} + xzq = y^2\]
\[ 2) (x+2z)p + (4zx-y)q = 2x^2+y\]

Answer 1

what defines a "solve"?

Answer 2

find the solution ..

Answer 3

are these exact equations by chance?

Answer 4

first order linear PDE ... i know how to solve them. just don't understand the solution.

Answer 5

according to book ... solution of
1) \( f(x^2-z^2, x^3-y^3) = 0\)
2) \( x^2-y-z =f(xy-z^2)\)
I have difficulty interpreting the last step.

Answer 6

*the solution are

Answer 7

\[ {y^2z \over x}dx + xz~dy = y^2\]
\[ {2y~z \over x} ;~ z\]

im having difficulty with the first step, so you one up on me :)

Answer 8

\[ \huge {y^2z \over x}{\partial z \over \partial x} + xz {\partial z \over \partial y} = y^2\]

Answer 9

Problem is i don't understand why the solution are of types

u and v are solution of