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Q.
The solution of $\frac{dy}{dx}+\frac{y}{x}=\frac{1}{\sqrt{1+x^{2}}}$ is
Differential Equations
Solution:
Given $\frac{dy}{dx}+\frac{y}{x}=\frac{1}{\sqrt{1+x^{2}}}$
It is linear differential equation with $I.F. =e^{\int \frac{1}{x}dx}=x$
$\therefore $ solution is, $y\cdot x=\int \frac{x}{\sqrt{1+x^{2}}}dx=\frac{1}{2}\int \frac{2x}{\sqrt{1+x^{2}}}dx$
$\Rightarrow y\cdot x=\sqrt{1+x^{2}}+c$
$\Rightarrow y=\frac{\sqrt{1+x^{2}}}{x}+\frac{c}{x}$