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Please solve RD Sharma Class 12 Chapter 21 Differential Equation Exercise Revision Exercise (RE) Question 47 maths textbook solution.

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Answer : \mathrm{y}+\mathrm{c}=\frac{\mathrm{a}}{2}[\log |x|-\log |x+2 a|]

Hint: you must know the rules of solving differential equation and integrations.

Given:  \left(2 a x+x^{2}\right) \frac{d y}{d x}=a^{2}

Solution : \left(2 a x+x^{2}\right) \frac{d y}{d x}=a^{2}

d y=\left(\frac{a^{2}}{\left(2 a x+x^{2}\right)}\right) d x


\begin{aligned} &d y=\left(\frac{a^{2}}{x(x+2 a)}\right) d x \\ &d y=\frac{a}{2}\left(\frac{1}{x}-\frac{1}{x+2 a}\right) d x \end{aligned}

Integrating both sides,

\begin{aligned} &\int d y=\frac{a}{2}\left[\int \frac{1}{x} d x-\int \frac{1}{x+2 a} d x\right] \\ &y+c=\frac{a}{2}[\log |x|-\log |x+2 a|] \end{aligned}



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