(a) Given $y' = x - y$ with $y(0) = 1$, compute $y(0.2)$ using Picard…

Question

(a) Given $y' = x - y$ with $y(0) = 1$, compute $y(0.2)$ using Picard's method.

(b) Using Euler's method, find an approximate value of $y$ at $x = 0.1$, given that $\frac{dy}{dx} = \frac{y - x}{y + x}$ and $y = 1$ when $x = 0$ taking $h = 0.02$.

(c) Use the Runge-Kutta method of fourth order to find $y(1.2)$ with $h = 0.1$ for the initial value problem $\frac{dy}{dx} = x^2 + y^2$, $y(1) = 1.5$.