Solve the differential equation
`(dy)/(dx)=sin^(4)x*cosx`.

Options

A. `y=(1)/(5)sin^(5)x+c`
B. `y=sin^(5)x+c`
C. `y=5sin^(5)x+c`
D. `y=-(1)/(5)sin^(5)x+c`

Answer

A

Explanation

`(dy)/(dx)=sin^(4)x*cosx`
Integrate both sides with respect to `x`
`int(dy)/(dx)*-dx=intsin^(4)x cosx dx+c`
Let `sinx=t`
`implies intdy=intt^(4)*-dt+-cimpliescosx=-(dt)/(dx)`
`cosxdx=dt`
`implies y=(1)/(5)t^(5)+c`
`implies y=(1)/(5)sin^(5)x+c`.