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

The solution for y^{''}+3y^'-3y=0 is y=c_{1}e^{((-3+sqrt(21))t)/2}+c_{2}e^{((-3-sqrt(21))t)/2}

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

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

y = c_{1} e^{\frac{( - 3 + 21 ) t}{2}} + c_{2} e^{\frac{( - 3 - 21 ) t}{2}}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{\frac{( - 3 + 21 ) t}{2}} + c_{2} e^{\frac{( - 3 - 21 ) t}{2}}

y = c_{1} e^{\frac{( - 3 + 21 ) t}{2}} + c_{2} e^{\frac{( - 3 - 21 ) t}{2}}

x^{^{''}} + 2 x^{^{'}} + 1^{2} x = 0

y^{^{''}} + 3 y^{^{'}} - 4 y = 0, y (0) = 5, y^{^{'}} (0) = 10

x^{^{''}} - 2 x^{^{'}} + 3 x = 0

2 y^{^{''}} + 5 y^{^{'}} - 3 y = 0, y (0) = 5, y^{^{'}} (0) = 13

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

What is the solution for y^{''}+3y^'-3y=0 ?
The solution for y^{''}+3y^'-3y=0 is y=c_{1}e^{((-3+sqrt(21))t)/2}+c_{2}e^{((-3-sqrt(21))t)/2}