What is the solution for y^{''}-y^'-11y=0 ?

The solution for y^{''}-y^'-11y=0 is y=c_{1}e^{((1+3sqrt(5))t)/2}+c_{2}e^{((1-3sqrt(5))t)/2}

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y^{''}-y^'-11y=0

y^{^{''}} - y^{^{'}} - 11 y = 0

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

Solution steps

y^{''} (t) - y^{'} (t) - 11 y = 0

Solve linear ODE:

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

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

What is the solution for y^{''}-y^'-11y=0 ?
The solution for y^{''}-y^'-11y=0 is y=c_{1}e^{((1+3sqrt(5))t)/2}+c_{2}e^{((1-3sqrt(5))t)/2}