# Let's do some calculus! (56)

Calculus Level 4

Let $f: \mathbb{R} \to \mathbb{R}$ given by $y = f(x)$ be a real-valued continuous function satisfying the differential equation

$\large \dfrac{d^3 y}{dx^3} - \dfrac{d^2 y}{dx^2} - \dfrac{dy}{dx} + y = 2e^x$

Given that $f(0)=0, f'(0)=1$ and $f''(0)=1$. Find the solution of the differential equation.