The solution of the differential equation y((sin)2 x)dy+(sin x cos ⁡ x)y2dx=xdx is (where C is the constant of integration)

Question

The solution of the differential equation y((sin)2 x)dy+(sin x cos ⁡ x)y2dx=xdx is (where C is the constant of integration) (A) sin2x⋅ y=x2+C (B) sin2x⋅ y2=x2+C (C) sinx⋅ y2=x2+C (D) sin2x⋅ y2=x+C

Tardigrade Admin · Accepted Answer

The given equation is (s i n2 x)(2 y d y)+(2 sin x cos ⁡ x d x)y2=2xdx or d(s i n2 x ⋅ y2)=2xdx On integrating, we get sin2x⋅ y2=x2+C

Q. The solution of the differential equation $y ((s in)^{2} x) d y + (s in x cos x) y^{2} d x = x d x$ is (where $C$ is the constant of integration)

$s i n^{2} x \cdot y = x^{2} + C$

$s i n^{2} x \cdot y^{2} = x^{2} + C$

$s in x \cdot y^{2} = x^{2} + C$

$s i n^{2} x \cdot y^{2} = x + C$

The given equation is $(s i n^{2} x) (2 y d y) + (2 s in x cos x d x) y^{2} = 2 x d x$
or $d (s i n^{2} x \cdot y^{2}) = 2 x d x$
On integrating, we get
$s i n^{2} x \cdot y^{2} = x^{2} + C$

Q. The solution of the differential equation y((sin)2x)dy+(sinxcos⁡x)y2dx=xdx is (where C is the constant of integration)

sin2x⋅y=x2+C

sin2x⋅y2=x2+C

sinx⋅y2=x2+C

sin2x⋅y2=x+C