Question

The solution of the differential equation $y\left(\left(sin\right)^{2} x\right)dy+\left(sin x cos ⁡ x\right)y^{2}dx=xdx$ is (where $C$ is the constant of integration)

• A. $sin^{2}x\cdot y=x^{2}+C$
• B. $sin^{2}x\cdot y^{2}=x^{2}+C$
• C. $sinx\cdot y^{2}=x^{2}+C$
• D. $sin^{2}x\cdot y^{2}=x+C$

Answer 1

Answer: (B)

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