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

The solution for y^{''}+y^'-8y=0 is y=c_{1}e^{((-1+sqrt(33))t)/2}+c_{2}e^{((-1-sqrt(33))t)/2}

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

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

y = c_{1} e^{\frac{( - 1 + 33 ) t}{2}} + c_{2} e^{\frac{( - 1 - 33 ) t}{2}}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{\frac{( - 1 + 33 ) t}{2}} + c_{2} e^{\frac{( - 1 - 33 ) t}{2}}

y = c_{1} e^{\frac{( - 1 + 33 ) t}{2}} + c_{2} e^{\frac{( - 1 - 33 ) t}{2}}

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

y^{^{''}} - 3 y^{^{'}} - 10 y = 0

y^{^{''}} + 14 y^{^{'}} + 49 y = 0, y (- 4) = - 1, y^{^{'}} (- 4) = 5

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

y^{^{''''}} - 4 y^{^{'''}} + 4 y^{^{''}} = 0

What is the solution for y^{''}+y^'-8y=0 ?
The solution for y^{''}+y^'-8y=0 is y=c_{1}e^{((-1+sqrt(33))t)/2}+c_{2}e^{((-1-sqrt(33))t)/2}