# Numerical Analysis/ODE Exercises

## Solve the following differential equations using the given method

### Euler's Method

1) Solve differential equation y' = 3t2y in [0,1] using Euler's method with n=10,y(0)=1.

### Runge-Kutta Second Order Method (RK2)

2) Solve differential equation y' = 2ty in [0,1] using RK2 method yn+1=yn+h/4(k1+3K2) where k1=f(tn,yn),k2=f(tn+2/3h,yn+2/3hk1)with n=5,y(0)=1.

4) Solve the ODE ${\displaystyle y'=2ty}$ on the interval ${\displaystyle [0,1]}$, using three steps of the Runge-Kutta 4 method with ${\displaystyle n=2}$ and ${\displaystyle y(0)=1}$.