Solving an ODE using Galerkin's method

[Breuno]

Homework Statement

Given the ODE \frac{df}{dt}=f and the boundary condition f(0)=1

One approximate solution is f_{a}=1+\sum ^{3}_{k=1} a_{k}t^k where 0\leq t\leq1

Using the Galerkin's method find the coeficents a_{k}

Homework Equations

The Attempt at a Solution

I don't think I've understood how to use the method really. So if someone could explain it briefly. Another thing that is mentioned in the book is that the basis funktions are not orthogonal on this interval. So that can not be imposed

Thanks
/Simon

 

[nasu]

You can take the derivative of the general (approximate) solution and plug in the equation.
Then equate the terms with the same power of t and you'll get 3 simple equations that will give you the three coefficients a1, a2, a3.