Author Topic: TUT5103  (Read 708 times)

Yuefan Wang

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TUT5103
« on: September 27, 2019, 02:00:01 PM »
Find the general solution of the equation:
$$
\begin{aligned} x y^{\prime} &=\left(1-y^{2}\right)^{\frac{1}{2}} \\ \frac{d y}{d x} x &=\sqrt{1-y^{2}} \\ \frac{1}{\sqrt{1-y^{2}}} & d y=\frac{1}{x} d x \\ \int \frac{1}{\sqrt{1-y^{2}}} d y &=\int \frac{1}{x} d x \\ \arcsin (y) &=\ln |x|+c \\ y &=\sin (\ln |x|+c) \end{aligned}
$$
when $x \neq 0, y \neq \pm 1$