What is the solution for y^{''}-3y^'-4y=5e^{-x},y(0)=1,y^'(0)=13 ?

The solution for y^{''}-3y^'-4y=5e^{-x},y(0)=1,y^'(0)=13 is y=3e^{4x}-2e^{-x}-e^{-x}x

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y^{''}-3y^'-4y=5e^{-x},y(0)=1,y^'(0)=13

y^{^{''}} - 3 y^{^{'}} - 4 y = 5 e^{- x}, y (0) = 1, y^{^{'}} (0) = 13

y = 3 e^{4 x} - 2 e^{- x} - e^{- x} x

Solution steps

y^{''} (x) - 3 y^{'} (x) - 4 y = 5 e^{- x}

Solve linear ODE:

y = 3 e^{4 x} - 2 e^{- x} - e^{- x} x

y = 3 e^{4 x} - 2 e^{- x} - e^{- x} x

y^{^{''}} - 4 y^{^{'}} + 4 y = e^{2 x} - 6

y^{^{''}} - y^{^{'}} - 2 y = 1 + t, y (0) = 2, y^{^{'}} (0) = 0

\frac{5}{3} y^{^{''}} + 10 y^{^{'}} + 30 y = 300

3 y^{^{''}} - 4 y^{^{'}} + y = x - 7

\frac{d ^{2} y}{d x ^{2}} + y = sec (x)

What is the solution for y^{''}-3y^'-4y=5e^{-x},y(0)=1,y^'(0)=13 ?
The solution for y^{''}-3y^'-4y=5e^{-x},y(0)=1,y^'(0)=13 is y=3e^{4x}-2e^{-x}-e^{-x}x