What is the solution for y^{''}-2y^'-3y=0,y(0)=3,y^'(0)=13 ?

The solution for y^{''}-2y^'-3y=0,y(0)=3,y^'(0)=13 is y=4e^{3t}-e^{-t}

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y^{''}-2y^'-3y=0,y(0)=3,y^'(0)=13

y^{^{''}} - 2 y^{^{'}} - 3 y = 0, y (0) = 3, y^{^{'}} (0) = 13

y = 4 e^{3 t} - e^{- t}

Solution steps

y^{''} (t) - 2 y^{'} (t) - 3 y = 0

Solve linear ODE:

y = 4 e^{3 t} - e^{- t}

y = 4 e^{3 t} - e^{- t}

y^{^{''}} + 12 y^{^{'}} + 27 y = 0

y^{^{'''}} - 6 y^{^{''}} - 15 y^{^{'}} + 100 y = 0

4 y^{^{''}} - 3 y^{^{'}} - 7 y = 0

y^{^{''}} + 4 y = 0, y (\frac{π}{6}) = 4, y^{^{'}} (\frac{π}{6}) = - 8

- y^{^{''}} + y^{^{'}} = 0

What is the solution for y^{''}-2y^'-3y=0,y(0)=3,y^'(0)=13 ?
The solution for y^{''}-2y^'-3y=0,y(0)=3,y^'(0)=13 is y=4e^{3t}-e^{-t}