Problem $3$:

Use the Runge$-$Kutta $($RK$4)$ method of numerical integration to solve the ODE:

$y^{\text{'}}=-2y^2+xy+x^2,$ where $y(0)=1$

Evaluate your solution for $x$ within $0,1$ using a timestep of $0\mathrm{.}05.($Hint: Modify the MATLAB code developed in class to solve this problem$)$

Use the dsolve function in MATLAB to get the exact solution of the ODE and generate a table of comparison of the numerical solution $($from the RK$4$ method$)$ and

the exact solution.