Solutions of the differential equation $\left( 1 - x^{2} \right)\frac{dy}{dx} + xy = ax$ where $a \i

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Solutions of the differential equation $\left( 1 - x^{2} \right)\frac{dy}{dx} + xy = ax$ where $a \in R$, is:

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Sol. (a,b,d)$$\begin{matrix} & \ - \int_{}^{}\ \frac{dy}{y - a} = \int_{}^{}\ \frac{x}{1 - x^{2}}dx \ \Rightarrow & \ - ln|y - a| = - \frac{1}{2}ln\left| 1 - x^{2} ight| - lnc^{2} \ \Rightarrow & \ (y - a)^{2} = c^{2}\left| 1 - x^{2} ight| \ & \frac{(y - a)^{2}}{c^{2}} + x^{2} = 1 \end{matrix}$$or $\ x^{2} - \frac{(y - a)^{2}}{c^{2}} = 1$

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