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## Homework Statement

Solve the following differential equation:

f"(x)=sinx

x(0)=0, x'(0)=1

## Homework Equations

x(0)=0, x'(0)=1

## The Attempt at a Solution

f"(x)=sin(x)

integrate,

f'(x)=-cos(x)+C1

f'(0)=-cos(0)+C1=1 => C1=2

C1=2

f'(x)=-cos(x)+2

f(x)=-sin(x)+2x+C2

f(0)=-sin(0)+C2=0 => C2=0

=>

f(x)=-sin(x)+2x