Write the differrntial equation representing famliy of curve y = … - Vidyadip

Question

Write the differrntial equation representing famliy of curve y = mx, where m is arbitrary constant.

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Answer

We have,
$\text{y}=\text{mx}\ ...(\text{i})$
Differentiating with respect to x,
$\Rightarrow \frac{\text{dy}}{\text{dx}}=\text{m}$
Substituting the value of $\frac{\text{dy}}{\text{dx}}=\text{m}$ in equation (i),
$\text{y}=\text{x}\frac{\text{dy}}{\text{dx}}$
Hence, $\text{y}=\text{x}\frac{\text{dy}}{\text{dx}}$ is the required differential equation.

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