Question

The solution of the differential equation $3sin^{2} xcos⁡xy^{2}dx+2ysin^{3}⁡xdy=sin⁡xdx$ is (where, $C$ is an arbitrary constant)

• A. $2y^{2}sin x=cos ⁡ x+C$
• B. $y^{2}sin^{3} x+cos ⁡ x=C$
• C. $y^{3}sin^{2} x+sin ⁡ x=C$
• D. $ysin x=cos^{2} ⁡ x+C$

Answer 1

Answer: (B)

The given equation is $d\left(y^{2} \left(sin\right)^{3} x\right)=sin ⁡ xdx$
On integrating, we get,
$\displaystyle \int d \left(y^{2} \left(sin\right)^{3} x\right)=\displaystyle \int sin ⁡ xdx$
$\Rightarrow y^{2}sin^{3} x=-cos ⁡ x+C$
or $y^{2}sin^{3} x+cos ⁡ x=C$