The general solution of the differential equation $\frac{d y}{d x}+\frac{1}{\sqrt{1-x^{2}}}=0$ is

The general solution of the differential equation $\frac{d y}{d x}+\frac{1}{\sqrt{1-x^{2}}}=0$ is
  1. $y^{2}+2 \sin ^{-1} x=c$
  2. $x+\sin ^{-1} y=c$
  3. $y+\sin ^{-1} x=c$
  4. $x^{2}+2 \sin ^{2} y=c$

Solution

$\frac{d y}{d x}+\frac{1}{\sqrt{1-x^{2}}}=0$ $\therefore \frac{d y}{d x}=\frac{-1}{\sqrt{1-x^{2}}} \Rightarrow d y=\frac{-d x}{\sqrt{1-x^{2}}} \Rightarrow \int d y=-\int \frac{d x}{\sqrt{1-x^{2}}}$ $\therefore y=-\sin ^{-1} x+c$

Asked in: MHT CET 2020 (14 Oct Shift 1)

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