Question

The solution of the differential equation $3si{n}^{2}xcosx{y}^{2}dx+2ysi{n}^{3}xdy=sinxdx$ is (where, $C$ is an arbitrary constant)

• A. $2y^{2}sinx=cosx+C$
• B. $y^{2}si{n}^{3}x+cosx=C$
• C. $y^{3}si{n}^{2}x+sinx=C$
• D. $ysinx=co{s}^{2}x+C$

Answer 1

Answer: (B)

The given equation is $d\left(y^2{\left(sin\right)}^{3}x\right)=sinxdx$
On integrating, we get,
$\int d\left(y^2{\left(sin\right)}^{3}x\right)=\int sinxdx$
$\Rightarrow y^{2}si{n}^{3}x=-cosx+C$
or $y^{2}si{n}^{3}x+cosx=C$