Question

the general solution of differential equation $x^4\frac{dy}{dx}+x^{3}y+cosecxy=0$, is

• A. 2 cos ( x y ) + $\frac{1}{x^2}$ = C
• B. 2 cos ( x y ) + $\frac{1}{y^2}$ = C
• C. 2 sin y + $\frac{1}{x^2}$ = C
• D. 2 sin ( x y ) + $\frac{1}{y^2}$ = C

Answer 1

The correct option is A 2 cos ( x y ) + $\frac{1}{x^2}$ = C

$x^{4}dy+x^{3}ydx+cosec\left(xy\right)dx=0$
$x^3(xdx+ydx)++cosec\left(xy\right)dx=0$
$\therefore \int \frac{d\left(xy\right)}{cosec\left(xy\right)}+\int \frac{dx}{x^3}=0$
$-cosxy+\frac{x^{-3+1}}{-3+1}=C$

$\therefore 2cos\left(xy\right)+\frac{1}{x^2}=C$