Question

The solution of $\frac{dy}{dx}=ysin\left(2x\right)$ given that $y\left(0\right)=0$

• A. $log\left|y\right|=si{n}^{2}x$
• B. $log\left|y\right|=sinx$
• C. $log\left|y\right|=sin2x$
• D. $log\left|y\right|=co{s}^{2}x$

Answer 1

The correct option is A $log\left|y\right|=si{n}^{2}x$

$\frac{dy}{dx}=ysin2x$

$\Rightarrow \int \frac{dy}{y}=\int sin2xdx-logC$

$\Rightarrow log|y|=\frac{-cos2x}{2}-logC$

$\Rightarrow log|y|=si{n}^{2}x-logC$