Solution of the differential equation (√1-x2 y2-y) d x=x d y is Where ' c ' is an arbitrary constant.

Question

Solution of the differential equation (√1-x2 y2-y) d x=x d y is Where ' c ' is an arbitrary constant. (A) y=( sin (x+c)/x) (B) x =( sin ( y + c )/ y ) (C) y=( cos (y+c)/x) (D) x=( tan (x+c)/y)

Tardigrade Admin · Accepted Answer

√1-x2 y2=x d y+y d x ; (d(x y)/√1-x2 y2)=1 sin -1(x y)=x+c ∴ y=( sin (x+c)/x)

Q. Solution of the differential equation $(1 - x^{2} y^{2} - y) d x = x d y$ is
Where ' $c$ ' is an arbitrary constant.

$y = \frac{s i n ( x + c )}{x}$

$x = \frac{s i n ( y + c )}{y}$

$y = \frac{c o s ( y + c )}{x}$

$x = \frac{t a n ( x + c )}{y}$

$1 - x^{2} y^{2} = x d y + y d x; \frac{d ( x y )}{1 - x ^{2} y ^{2}} = 1$
$sin^{- 1} (x y) = x + c$
$∴ y = \frac{s i n ( x + c )}{x}$

Q. Solution of the differential equation (1−x2y2​−y)dx=xdy is Where ' c ' is an arbitrary constant.

y=xsin(x+c)​

x=ysin(y+c)​

y=xcos(y+c)​

x=ytan(x+c)​