The general solution of (d y/d x)=√1-x2-y2+x2 y2 is

Question

The general solution of (d y/d x)=√1-x2-y2+x2 y2 is (A) 2 sin -1 y=x √1-x2+ sin -1 x+c (B)  cos -1 y=x cos -1 x+c (C)  sin -1 y=(1/2) sin -1 x+c (D) 2 sin -1 y=x √1-y2+c

Tardigrade Admin · Accepted Answer

(d y/d x)=√1-x2-y2+x2 y2 =√(1-x2)(1-y2) (d y/√1-y2)=√1-x2 . d x sin -1 y=(x/2) √1-x2+(1/2) sin -1 x+ c 2 sin -1 y=x √1-x2+ sin -1 x +c

Q. The general solution of $\frac{d y}{d x} = 1 - x^{2} - y^{2} + x^{2} y^{2}$ is

$2 sin^{- 1} y = x 1 - x^{2} + sin^{- 1} x + c$

$cos^{- 1} y = x cos^{- 1} x + c$

$sin^{- 1} y = \frac{1}{2} sin^{- 1} x + c$

$2 sin^{- 1} y = x 1 - y^{2} + c$

$\frac{d y}{d x} = 1 - x^{2} - y^{2} + x^{2} y^{2}$
$= (1 - x^{2}) (1 - y^{2})$
$\frac{d y}{1 - y ^{2}} = 1 - x^{2} . d x$
$sin^{- 1} y = \frac{x}{2} 1 - x^{2} + \frac{1}{2} sin^{- 1} x + c$
$2 sin^{- 1} y = x 1 - x^{2} + sin^{- 1} x + c$

Q. The general solution of dxdy​=1−x2−y2+x2y2​ is

2sin−1y=x1−x2​+sin−1x+c

cos−1y=xcos−1x+c

sin−1y=21​sin−1x+c

2sin−1y=x1−y2​+c