Solve the following differential equation:

Question

f"(x)=sinx, x(0)=0, x'(0)=1

Answer 1

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