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Please solve RD Sharma class 12 chapter Differential Equation exercise 21.3 question 21 sub question (i) maths textbook solution

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Answer:

The given function is the solution to the given differential equation.

Hint:

Just differentiate the given function to obtain differential equation.

Given:

y=ax 

Solution:

\Rightarrow y=a x

Differentiating above equation

\Rightarrow \frac{d y}{d x}=a                                            ...........(i)

Now from y=ax

a=\frac{y}{x}

Substitute (ii) in (i)

\begin{aligned} &\Rightarrow \frac{d y}{d x}=\frac{y}{x} \\\\ &\Rightarrow x \cdot \frac{d y}{d x}=y \end{aligned}

Hence, the given function is the solution to the given differential equation.

 

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