What is the solution for y^{''}-6y^'-7y=0,y(0)=4,y^'(0)=4 ?

The solution for y^{''}-6y^'-7y=0,y(0)=4,y^'(0)=4 is y=e^{7t}+3e^{-t}

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y^{''}-6y^'-7y=0,y(0)=4,y^'(0)=4

y^{^{''}} - 6 y^{^{'}} - 7 y = 0, y (0) = 4, y^{^{'}} (0) = 4

y = e^{7 t} + 3 e^{- t}

Solution steps

y^{''} (t) - 6 y^{'} (t) - 7 y = 0

Solve linear ODE:

y = e^{7 t} + 3 e^{- t}

y = e^{7 t} + 3 e^{- t}

y^{^{''}} - 6 y^{^{'}} + 25 y = 0, y (0) = 2, y^{^{'}} (0) = - 2

(4 D^{4} - 4 D^{3} - 23 D^{2} + 12 D + 36) y = 0

2500 y^{^{''}} - 9 y = 0, y (0) = 6, y^{^{'}} (0) = 7

\frac{d ^{3} x}{d t ^{3}} - x = 0

16 y^{^{''}} - 72 y^{^{'}} + 81 y = 0, y^{^{'}} (0) = 8

What is the solution for y^{''}-6y^'-7y=0,y(0)=4,y^'(0)=4 ?
The solution for y^{''}-6y^'-7y=0,y(0)=4,y^'(0)=4 is y=e^{7t}+3e^{-t}