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Solve the first order partial differential equation xp+yq=3z

Answers (1)

best_answer

The equation is,

x \frac{\partial z}{\partial x}+y \frac{\partial z}{\partial y}=3 z

\frac{d x}{x}=\frac{d y}{y}=\frac{d z}{3 z}

Upon solving the equation, we get,

\begin{aligned} & \frac{x}{y}=C_1 \\ & x^3=C_2 z \end{aligned}

The final answer is.

z=C \frac{x^3}{y}

Posted by

Divya Sharma

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