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Differential Equations — Maths STD 12 Science — Question

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

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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