Use separation of variables to find the general solution of the differential equation.

Question

​Use separation of variables to find the general solution of the differential equation. ​  ​

Quizplus · Accepted Answer

The differential equation  $\frac{dy}{dx}=\frac{2y}{3x}$ can be written as $\frac{dy}{y}=\frac{2dx}{3x}$.
Using separation of variables,
$\int \frac{dy}{y}=\int\frac{2dx}{3x}$
$\ln|y|=\frac23\ln |x|+c$
$|y|=e^{\frac23\ln |x|+c}$
$|y|=e^{\ln |x^{\frac23}|+c}$
$|y|=k|x^{\frac23}|$
Therefore, the general solution of the given differential equation is $y=kx^{\frac23}$.

​Use Separation of Variables to Find the General Solution of the Differential

Use Separation of Variables to Find the General Solution of the Differential