What is the solution for (d^2y)/(dx^2)=4e^{-x},y(0)=3,y^'(0)=2 ?

The solution for (d^2y)/(dx^2)=4e^{-x},y(0)=3,y^'(0)=2 is y=4e^{-x}+6x-1

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(d^2y)/(dx^2)=4e^{-x},y(0)=3,y^'(0)=2

\frac{d ^{2} y}{d x ^{2}} = 4 e^{- x}, y (0) = 3, y^{^{'}} (0) = 2

y = 4 e^{- x} + 6 x - 1

Solution steps

y^{''} (x) = 4 e^{- x}

Solve

y^{''} (x) = 4 e^{- x} : y^{'} (x) = - 4 e^{- x} + c_{1}

Solve

y^{'} (x) = - 4 e^{- x} + c_{1} : y = 4 e^{- x} + c_{1} x + c_{2}

Apply initial conditions:

y = 4 e^{- x} + 6 x - 1

y = 4 e^{- x} + 6 x - 1

\frac{1}{2 r} + \frac{1}{3 r ^{\frac{2}{3}}}

y \to \infty lim (\frac{1}{5} (2 y^{2} + 3 y) x)

2 - x^{2}, 10 - 6 x

\int_{0}^{0.4} 300 x d x

What is the solution for (d^2y)/(dx^2)=4e^{-x},y(0)=3,y^'(0)=2 ?
The solution for (d^2y)/(dx^2)=4e^{-x},y(0)=3,y^'(0)=2 is y=4e^{-x}+6x-1