Question

Write an algorithm (i.e. the series of steps) to find the solution to a second order non-homogenous ODE (with boundary conditions) using the method of undetermined coefficients. (Note: this algorithm should include at least 1 control structure).

Answer 1

let ay''+by'+c = r(x) be the  second order non-homogenous ODE

steps are as below:-

1. find the general solution(Yc) to the homogeneous part of the differential equation(i.e ay''+by'+c =0)
2. find(or guess) a particular solution for the above equation Yp.
3. the general solution is the sum of the above two solutions i.e Y=Yc+Yp
4. put the boundary values in the equation of Y(found in the last step) to find the unknown coefficients in Yc.
5. The final answer is Y with the unknown coefficients replaces with their found values.