What is the solution for 2y^{''}-17y^'-9y=0,y(0)=4,y^'(0)=-7 ?

The solution for 2y^{''}-17y^'-9y=0,y(0)=4,y^'(0)=-7 is y=(4-86/19)e^{9t}+86/19 e^{-t/2}

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2y^{''}-17y^'-9y=0,y(0)=4,y^'(0)=-7

2 y^{^{''}} - 17 y^{^{'}} - 9 y = 0, y (0) = 4, y^{^{'}} (0) = - 7

y = (4 - \frac{86}{19}) e^{9 t} + \frac{86}{19} e^{- \frac{t}{2}}

Solution steps

2 y^{''} (t) - 17 y^{'} (t) - 9 y = 0

Solve linear ODE:

y = (4 - \frac{86}{19}) e^{9 t} + \frac{86}{19} e^{- \frac{t}{2}}

y = (4 - \frac{86}{19}) e^{9 t} + \frac{86}{19} e^{- \frac{t}{2}}

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

y^{^{''}} + 2 y^{^{'}} + y = 0, y (0) = 1, y^{^{'}} (0) = - 5

u^{^{''}} = H (t)

0.25 \cdot 0.04 x^{^{''}} + 2 \cdot 0.04 x^{^{'}} + x = 0

y^{^{''}} + 20 y^{^{'}} + 92 y = 0

What is the solution for 2y^{''}-17y^'-9y=0,y(0)=4,y^'(0)=-7 ?
The solution for 2y^{''}-17y^'-9y=0,y(0)=4,y^'(0)=-7 is y=(4-86/19)e^{9t}+86/19 e^{-t/2}