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

The solution for y^{''}-3y^'-4y=0,y(0)=0,y^'(0)=1 is y= 1/5 e^{4t}-1/5 e^{-t}

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y^{''}-3y^'-4y=0,y(0)=0,y^'(0)=1

y^{^{''}} - 3 y^{^{'}} - 4 y = 0, y (0) = 0, y^{^{'}} (0) = 1

y = \frac{1}{5} e^{4 t} - \frac{1}{5} e^{- t}

Solution steps

y^{''} (t) - 3 y^{'} (t) - 4 y = 0

Solve linear ODE:

y = \frac{1}{5} e^{4 t} - \frac{1}{5} e^{- t}

y = \frac{1}{5} e^{4 t} - \frac{1}{5} e^{- t}

y^{^{''}} + y^{^{'}} = 0, y (\frac{π}{4}) = 0, y^{^{'}} (\frac{π}{4}) = - 3

y^{^{''}} + (\frac{v}{a}) y^{^{'}} = 0

\frac{d ^{4} y}{d x ^{4}} - 2 (\frac{d ^{2} y}{d x ^{2}}) + y = 0

y^{^{''}} - 16 y = 0, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} - 7 y^{^{'}} = 0, y (0) = 2 - 2 e^{7}, y (1) = 0

What is the solution for y^{''}-3y^'-4y=0,y(0)=0,y^'(0)=1 ?
The solution for y^{''}-3y^'-4y=0,y(0)=0,y^'(0)=1 is y= 1/5 e^{4t}-1/5 e^{-t}