Let's do some calculus! (56)

Calculus Level 5

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

d3ydx3d2ydx2dydx+y=2ex\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)=1f(0)=0, f'(0)=1 and f(0)=1f''(0)=1. Find the solution of the differential equation.

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