What is the solution for y^{''}-4y^'-5y=0,y(0)=2,y^'(0)=4 ?

The solution for y^{''}-4y^'-5y=0,y(0)=2,y^'(0)=4 is y=e^{5t}+e^{-t}

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y^{''}-4y^'-5y=0,y(0)=2,y^'(0)=4

y^{^{''}} - 4 y^{^{'}} - 5 y = 0, y (0) = 2, y^{^{'}} (0) = 4

y = e^{5 t} + e^{- t}

Solution steps

y^{''} (t) - 4 y^{'} (t) - 5 y = 0

Solve linear ODE:

y = e^{5 t} + e^{- t}

y = e^{5 t} + e^{- t}

y^{^{''}} + 100 y = 0, y (0) = - \frac{2}{3}, y^{^{'}} (0) = 5

y^{^{'''}} + 6 y^{^{''}} + 8 y^{^{'}} = 0

y^{^{''}} - y^{^{'}} = 0, y^{^{'}} (0) = 1, y (0) = 0

y^{^{''}} + 8 y^{^{'}} + \frac{1}{2} y = 0

x^{^{''}} - 7 x^{^{'}} + 4 x = 0

What is the solution for y^{''}-4y^'-5y=0,y(0)=2,y^'(0)=4 ?
The solution for y^{''}-4y^'-5y=0,y(0)=2,y^'(0)=4 is y=e^{5t}+e^{-t}