What is the solution for y^{''}-8y^{''}+16y=0 ?

The solution for y^{''}-8y^{''}+16y=0 is y=c_{1}e^{(4t)/(sqrt(7))}+c_{2}e^{-(4t)/(sqrt(7))}

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y^{''}-8y^{''}+16y=0

y^{^{''}} - 8 y^{^{''}} + 16 y = 0

y = c_{1} e^{\frac{4 t}{7}} + c_{2} e^{- \frac{4 t}{7}}

Solution steps

y^{''} (t) - 8 y^{''} (t) + 16 y = 0

Solve linear ODE:

y = c_{1} e^{\frac{4 t}{7}} + c_{2} e^{- \frac{4 t}{7}}

y = c_{1} e^{\frac{4 t}{7}} + c_{2} e^{- \frac{4 t}{7}}

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

6 y^{^{''}} + (- 5) y^{^{'}} + y = 0, y (0) = 4, y^{^{'}} (0) = 0

y^{^{''}} - 2 y^{^{'}} + 13 y = 0

y^{^{''}} - 22 y^{^{'}} = 0

y^{^{''}} + 9 y^{^{'}} + 17 y = 0

What is the solution for y^{''}-8y^{''}+16y=0 ?
The solution for y^{''}-8y^{''}+16y=0 is y=c_{1}e^{(4t)/(sqrt(7))}+c_{2}e^{-(4t)/(sqrt(7))}