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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + 8 y^{^{'}} + 160 y = 0

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

y^{^{''}} + 0.2 y^{^{'}} + 0.01 y = 0

y^{^{''}} + 9 y^{^{'}} - 20 y = 0, y (0) = 1, y^{^{'}} (0) = 2

y^{^{''''}} + 5 y^{^{'''}} = 0

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