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  • Provide solution for RD Sharma maths class 12 chapter Differential Equation exercise 21.2 question 16 subquestion (x)

Provide solution for RD Sharma maths class 12 chapter Differential Equation exercise 21.2 question 16 subquestion (x)

Answers (1)

Answer:

 The required equation is

x\frac{\mathrm{d} y}{\mathrm{d} x}=y\, log\, y

Hint:

 Differentiating the given equation with respect to x

Given:

 y=e^{ax}

Solution:

y=e^{ax}

Differentiating with respect to x

\begin{aligned} &\frac{\mathrm{d} y}{\mathrm{d} x}=ae^{ax} \\ &\frac{\mathrm{d} y}{\mathrm{d} x}=ay \end{aligned}

From the given equation, we have

\begin{aligned} &y=e^{ax} \\ &log\, y=ax \\&a=\frac{log\, y}{x} \end{aligned}

Now,

\begin{aligned} &\frac{\mathrm{d} y}{\mathrm{d} x}=ay=y\frac{log\, y}{x} \\ &x\frac{\mathrm{d} y}{\mathrm{d} x}=y\, log\, y\end{aligned}

 The required equation is

x\frac{\mathrm{d} y}{\mathrm{d} x}=y\, log\, y

Posted by

Gurleen Kaur

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