What is the solution for y^{''}-y^'-20y=0,y(0)=-1,y^'(0)=49 ?

The solution for y^{''}-y^'-20y=0,y(0)=-1,y^'(0)=49 is y=5e^{5t}-6e^{-4t}

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y^{''}-y^'-20y=0,y(0)=-1,y^'(0)=49

y^{^{''}} - y^{^{'}} - 20 y = 0, y (0) = - 1, y^{^{'}} (0) = 49

y = 5 e^{5 t} - 6 e^{- 4 t}

Solution steps

y^{''} (t) - y^{'} (t) - 20 y = 0

Solve linear ODE:

y = 5 e^{5 t} - 6 e^{- 4 t}

y = 5 e^{5 t} - 6 e^{- 4 t}

y^{^{''}} - y = 0, y (0) = e^{t}, y (0) = cosh (t)

2 y^{^{''}} - y^{^{'}} - 15 y = 0

y^{^{''}} - 6 y = 0, y (0) = 13, y^{^{'}} (0) = 0

\frac{d ^{2} y}{d x ^{2}} (1) - \frac{d y}{d x} (1) - 2 y = 0

y^{^{'''}} - 15 y^{^{''}} + 62 y^{^{'}} - 72 y = 0

What is the solution for y^{''}-y^'-20y=0,y(0)=-1,y^'(0)=49 ?
The solution for y^{''}-y^'-20y=0,y(0)=-1,y^'(0)=49 is y=5e^{5t}-6e^{-4t}