The general solution of the differential equation d y d x =y x is - Vidyadip

Question

The general solution of the differential equation $\frac{d y}{d x}=\frac{y}{x}$ is

✓

Answer

$(a) y = kx$
Explanation: We have,
$\frac{d y}{d x}=\frac{y}{x}$
$\Rightarrow \frac{d y}{y}=\frac{d x}{x}$
Integrating on both sides,
$\int \frac{d y}{y}=\int \frac{d x}{x}$
$\log |y|=\log |x|+\log k$
$\Rightarrow \log \left(\frac{y}{x}\right)=\log k$
$\Rightarrow y = kx $

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