1. Write a python code that uses the Runge Kutta Method method
to approximate the solutions to each of the following initial-value
problems and compare/plot the results to the actual values.
a) y′=te^(3t) − 2y, 0 < t < 1, y(0) = 0
with h = 0.5; actual solution y(t)=1/5te^(3t) − 1/25e^(3t) +
1/25e^(−2t).
- Use the Runge Kutta method to approximate/plot the solutions
to each of the following initial-value
b) ?′=1+(?−?)2,2<?<3,?(2)=1y′=1+(t−y)2,2
c) ?′=1+??,1<?<1,?(1)=2y′=1+yt,1