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

The solution for y^{''}+3y^'-y=0 is y=c_{1}e^{((-3+sqrt(13))t)/2}+c_{2}e^{((-3-sqrt(13))t)/2}

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

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

y = c_{1} e^{\frac{( - 3 + 13 ) t}{2}} + c_{2} e^{\frac{( - 3 - 13 ) t}{2}}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{\frac{( - 3 + 13 ) t}{2}} + c_{2} e^{\frac{( - 3 - 13 ) t}{2}}

y = c_{1} e^{\frac{( - 3 + 13 ) t}{2}} + c_{2} e^{\frac{( - 3 - 13 ) t}{2}}

What is the solution for y^{''}+3y^'-y=0 ?
The solution for y^{''}+3y^'-y=0 is y=c_{1}e^{((-3+sqrt(13))t)/2}+c_{2}e^{((-3-sqrt(13))t)/2}