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Explain solution RD Sharma class 12 chapter Differential Equation exercise 21.2 question 16 subquestion (viii) maths

Answers (1)

Answer:

 The required equation is

x\frac{\mathrm{d} y}{\mathrm{d} x}=3y

Hint:

 Differentiating the given equation with respect to x

Given:

 y=ax^{3}

Solution:

y=ax^{3}

On differentiating with respect to x, we get

\frac{\mathrm{d} y}{\mathrm{d} x}=3ax^{2}

From the given equation,

a=\frac{y}{x^{3}}

So, we have

\begin{aligned} &\frac{\mathrm{d} y}{\mathrm{d} x}=3\frac{y}{x^{3}}(x^{2})\\ &\frac{\mathrm{d} y}{\mathrm{d} x}=\frac{3y}{x} \\ &x\frac{\mathrm{d} y}{\mathrm{d} x}=3y \end{aligned}

 The required equation is

x\frac{\mathrm{d} y}{\mathrm{d} x}=3y

Posted by

Gurleen Kaur

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