Author Topic: TUT0401 QUIZ1  (Read 500 times)

Yuying Chen

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TUT0401 QUIZ1
« on: September 27, 2019, 02:15:53 PM »
$x{y^\prime } = {\left( {1 - {y^2}} \right)^{1/2}}.$


$\qquad$$\qquad$$\therefore Separable$

$\qquad$$\qquad$$\therefore x \frac{d y}{d x}=\sqrt{1-y^{2}}$

$\qquad$$\qquad$$Rearrange:~\int \frac{1}{\sqrt{1-y^{2}}} d y=\int \frac{1}{x} d x \quad~where~x \neq 0, y \neq \pm 1$

$\qquad\qquad {Integrating on both side}:$

$\qquad\qquad LHS:\int \frac{1}{\sqrt{1-y^{2}}}=\arcsin y=\ln |y|+C$

$\qquad\qquad RHS:\int \frac{1}{x} d x=\ln |x|$

$\qquad\qquad \therefore~General~sol:\arcsin y=\ln|x|+C$

$\qquad\qquad\qquad\qquad\qquad\qquad\qquad y=\sin ( \ln |x |+C) \quad x \neq 0 \quad y \neq \pm 1$