What is the solution for y^{''}+3y^'-9y=0 ?

The solution for y^{''}+3y^'-9y=0 is y=c_{1}e^{((-3+3sqrt(5))t)/2}+c_{2}e^{((-3-3sqrt(5))t)/2}

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y^{''}+3y^'-9y=0

y^{^{''}} + 3 y^{^{'}} - 9 y = 0

y = c_{1} e^{\frac{( - 3 + 3 5 ) t}{2}} + c_{2} e^{\frac{( - 3 - 3 5 ) t}{2}}

Solution steps

y^{''} (t) + 3 y^{'} (t) - 9 y = 0

Solve linear ODE:

y = c_{1} e^{\frac{( - 3 + 3 5 ) t}{2}} + c_{2} e^{\frac{( - 3 - 3 5 ) t}{2}}

y = c_{1} e^{\frac{( - 3 + 3 5 ) t}{2}} + c_{2} e^{\frac{( - 3 - 3 5 ) t}{2}}

100 y^{^{''}} + 90 y^{^{'}} - 162 y = 0

y^{^{''}} - 4 y^{^{'}} - 13 y = 0

\frac{3}{4} \frac{d ^{2} x}{d t ^{2}} + 72 x = 0, x (0) = - \frac{1}{2}

y^{^{''}} - 16 y^{^{'}} + 73 y = 0

y^{^{''}} - 8 y^{^{'}} + 9 y = 0, y (0) = 0, y^{^{'}} (0) = 3

What is the solution for y^{''}+3y^'-9y=0 ?
The solution for y^{''}+3y^'-9y=0 is y=c_{1}e^{((-3+3sqrt(5))t)/2}+c_{2}e^{((-3-3sqrt(5))t)/2}