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Differential Equations — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSDifferential Equations2 Marks
Question
For the following differntial equations verify that the accompanying function is a solution:
Differential equation Function
$\text{x}\frac{\text{dy}}{\text{dx}}=\text{y}$ $\text{y}=\text{ax}$
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Answer

We have $\text{y}=\text{ax}\ ...(1)$ Given differential equation Differentiating both sides of (1) with respect to x, we get $\frac{\text{dy}}{\text{dx}}=\text{a}$ $\Rightarrow\frac{\text{dy}}{\text{dx}}=\frac{\text{y}}{\text{x}}$ $\Rightarrow\text{x}\frac{\text{dy}}{\text{dx}}={\text{y}}$Hence, the given function is the solution to the given differential equation.

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