Solving differential equations

  • Thread starter chapsticks
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  • #1
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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
 

Answers and Replies

  • #2
ehild
Homework Helper
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It is correct.

ehild
 
  • #3
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7,271

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?
 

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