What is the solution for y^{''}-2y^'-3y=0,y(4)=-17 ?

The solution for y^{''}-2y^'-3y=0,y(4)=-17 is y=e^{3t-16}(-17e^4-c_{2})+c_{2}e^{-t}

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y^{''}-2y^'-3y=0,y(4)=-17

y^{^{''}} - 2 y^{^{'}} - 3 y = 0, y (4) = - 17

y = e^{3 t - 16} (- 17 e^{4} - c_{2}) + c_{2} e^{- t}

Solution steps

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

Solve linear ODE:

y = e^{3 t - 16} (- 17 e^{4} - c_{2}) + c_{2} e^{- t}

y = e^{3 t - 16} (- 17 e^{4} - c_{2}) + c_{2} e^{- t}

y^{^{'''}} + (- 7) y^{^{''}} + 8 y^{^{'}} + 16 y = 0

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

y^{^{''}} + a^{2} b^{2} y = 0

y^{^{''}} + 4 y^{^{'}} - 5 y = 0, y^{^{'}} (ln (2)) = 3, y (0) = 33

\frac{d ^{2} x}{d t ^{2}} - 49 x = 0, x = 2

What is the solution for y^{''}-2y^'-3y=0,y(4)=-17 ?
The solution for y^{''}-2y^'-3y=0,y(4)=-17 is y=e^{3t-16}(-17e^4-c_{2})+c_{2}e^{-t}