Answer to Question #323853 in Differential Equations for Ramya

Question

Solve 𝑧𝑝 = −𝑥.

Answer 1

$𝑧𝑝 = −𝑥$

$p=\frac{dz}{dx}$

$𝑧\frac{dz}{dx} = −𝑥$

$zdz=-xdx$

$\frac{z^2}{2}=-\frac{x^2}{2}+\frac C2$

$z^2+x^2=C$

Answer: $z^2+x^2=C$ .