That makes a lot of sense. Just working through it now, but I think it was realising I *had* reduced the order and had a first order ODE and then solving with the integrating factor was the point I was missing.
Thanks very much.
Homework Statement
Solving the linked set of ODEs:
y" + y = 1-t^2/π^2 for 0 ≤ t ≤ π
y" + y = 0 for t > π
We are given the initial condition that y(0) = y'(0) = 0, and it is also noted that y and y' must be continuous at t = π
Homework Equations
See above.
The Attempt at a...
Homework Statement
Question is to find a general solution, using reduction of order to:
(1-x^2)y" - 2xy' +2y = 0
(Legendre's differential equation for n=1)
Information is given that the Legendre polynomials for the relevant n are solutions, and for n=1 this means 'x' is a solution...