Solving differential equations

[chapsticks]

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

 

[ehild]

It is correct.

ehild

 

[Mark44]

Homework Statement

Solve the following differential equation:

f"(x)=sinx

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

Minor point, but this should be f(0) = 0, f'(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

What's your question?