The solution of the differential equation (d y/d x) = (y c o s x - y2/sin x) is equal to (where c is an arbitrary constant)

Question

The solution of the differential equation (d y/d x) = (y c o s x - y2/sin x) is equal to (where c is an arbitrary constant) (A) sin x=x-y+c (B) sin x=x+y+c (C) sin x=xy+cy (D) (sin x/x)=y+c

Tardigrade Admin · Accepted Answer

(d y/d x)=(y c o s x - y2/sin x) ycos xdx-sinâ¡xdy=y2dx (y c o s x . d x - sin x . d y/y2)=dx d((sin x/y))=dx On integrating, we get, (sin x/y)=x+c sin x=xy+cy

Q. The solution of the differential equation $\frac{d y}{d x}$ = $\frac{ycos x - y ^{2}}{s in x}$ is equal to (where $c$ is an arbitrary constant)

$s in x = x - y + c$

$s in x = x + y + c$

$s in x = x y + cy$

$\frac{s in x}{x} = y + c$

$\frac{d y}{d x} = \frac{ycos x - y ^{2}}{s in x}$
$ycos x d x - s in x d y = y^{2} d x$
$\frac{ycos x . d x - s in x . d y}{y ^{2}} = d x$
$d (\frac{s in x}{y}) = d x$
On integrating, we get,
$\frac{s in x}{y} = x + c$
$s in x = x y + cy$

Q. The solution of the differential equation dxdy​ = sinxycosx−y2​ is equal to (where c is an arbitrary constant)

sinx=x−y+c

sinx=x+y+c

sinx=xy+cy

xsinx​=y+c