[latex]
\[
\textbf{Solve the Differential Equation:} \quad x \frac{dy}{dx} = 4y
\]
Solution:
\[
\textbf{Step 1: Rewrite the equation}
\]
\[
\frac{1}{y} \, dy = \frac{4}{x} \, dx
\]
\[
\textbf{Step 2: Integrate both sides}
\]
\[
\int \frac{1}{y} \, dy = \int \frac{4}{x} \, dx
\]
\[
\textbf{Step 3: Solve the integrals}
\]
\[
\ln|y| = 4 \ln|x| + C
\]
\[
\textbf{Step 4: Simplify}
\]
\[
\ln|y| = \ln|x^4| + C
\]
\[
y = C_1 x^4
\]
\[
\textbf{Final Solution:}
\]
\[
y = C x^4
\]