Solve the initial value problem.
-$$\frac { d y } { d x } = 15 \sin ^ { 2 } x \cos x , y ( 0 ) = 2$$
A) $y = 5 \sin ^ { 3 } x + 2$
B) $y = \frac { 15 } { 2 } \cos 2 x + 2$
C) $y = - 5 \sin ^ { 3 } x - 2$
D) $y = 30 \sin x \cos x + 2$

Question

Quizplus · Accepted Answer

The given differential equation is $\frac { d y } { d x } = 15 \sin ^ { 2 } x \cos x$. Integrating both sides with respect to $x$, we get $y = 5 \sin^3 x + C$. Using the initial condition $y(0) = 2$, we find $C = 2$, so the solution is $y = 5 \sin^3 x + 2$.

Solve the Initial Value Problem dydx=15sin⁡2xcos⁡x,y(0)=2\frac { d y } { d x } = 15 \sin ^ { 2 } x \cos x , y ( 0 ) = 2dxdy​=15sin2xcosx,y(0)=2

Solve the Initial Value Problem $\frac { d y } { d x } = 15 \sin ^ { 2 } x \cos x , y ( 0 ) = 2$