What is the solution for y^{''}+3y^'-6y=0 ?

The solution for y^{''}+3y^'-6y=0 is y=c_{1}e^{((-3+sqrt(33))t)/2}+c_{2}e^{((-3-sqrt(33))t)/2}

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y^{''}+3y^'-6y=0

y^{^{''}} + 3 y^{^{'}} - 6 y = 0

y = c_{1} e^{\frac{( - 3 + 33 ) t}{2}} + c_{2} e^{\frac{( - 3 - 33 ) t}{2}}

Solution steps

y^{''} (t) + 3 y^{'} (t) - 6 y = 0

Solve linear ODE:

y = c_{1} e^{\frac{( - 3 + 33 ) t}{2}} + c_{2} e^{\frac{( - 3 - 33 ) t}{2}}

y = c_{1} e^{\frac{( - 3 + 33 ) t}{2}} + c_{2} e^{\frac{( - 3 - 33 ) t}{2}}

y^{^{''}} - 4 y^{^{'}} - 5 y = 0, y (0) = 1, y^{^{'}} (0) = 2

y^{^{'''}} + 5 y^{^{''}} - 13 y^{^{'}} + 7 y = 0

0.05 y^{^{''}} + 2 y^{^{'}} + 100 y = 0, y (0) = 5, y^{^{'}} (0) = 0

(D^{4} - 81) y = 0

y^{^{''}} + y = 0, y (0) = 3, y (1) = - 3

What is the solution for y^{''}+3y^'-6y=0 ?
The solution for y^{''}+3y^'-6y=0 is y=c_{1}e^{((-3+sqrt(33))t)/2}+c_{2}e^{((-3-sqrt(33))t)/2}