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Given the second-order differential equation y''(x) − xy'(x) + x^2 y(x) = 0 with initial conditions...

Given the second-order differential equation

y''(x) − xy'(x) + x^2 y(x) = 0

with initial conditions
y(0) = 0, y'(0) = 1.

(a) Write this equation as a system of 2 first order differential equations.

(b) Approximate its solution by using the forward Euler method.

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