Question

Solution of zp=-x in PDE

Answer 1

Answer: x2+y2=phi(y)

This is the correct answer.Trying to find the steps.

Answer 2

Answer:

$x^{2} + z^{2}=C$ is the solution of the equation $zp=-x$.

Step-by-step explanation:

Consider the partial differential equation as follows:

$zp=-x$

The auxiliary equation is

$\frac{dx}{z} = \frac{dz}{-x}$

Using method of variable separable.

$-xdx=zdz$

Integrating both the side as follows:

$-\frac{x^{2}}{2} = \frac{z^{2}}{2}+C_{1}$, where $C_{1}$ is the integration constant.

⇒ $-\frac{x^{2}}{2} - \frac{z^{2}}{2}=C_{1}$

⇒ $x^{2} + z^{2} =-2C_{1}$

⇒ $x^{2} + z^{2}=C$, where $C=-2C_{1}$.

Therefore, the solution of the equation $zp=-x$ is $x^{2} + z^{2}=C$.

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