Question

Solve the differential Equation x^2+p^2x=yp​

Answer 1

$-1py+p^2+x^2=0$ is the solution.

Simplifying

$x^2 +p^2x=yp$

Reorder the terms:

$p^2x+x^2=yp$

$p^2x+x^2=py$

Solving for variable 'p'.

$-1py+p^2x+x^2=py-1py$

Combine like terms: py + -1py = 0

$-1py+p^2+x^2=0$

The solution to this equation could not be determined.

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Answer 2

Answer:

x=-1/3 p^3+cp^1/2,y=(-1/3 p^2+cp^1/2)^2 /p+p^2(-1/3 p^2+cp^1/2)