What is the solution for y^{''}+3y^'-12y=0 ?

The solution for y^{''}+3y^'-12y=0 is y=c_{1}e^{((-3+sqrt(57))t)/2}+c_{2}e^{((-3-sqrt(57))t)/2}

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y^{''}+3y^'-12y=0

y^{^{''}} + 3 y^{^{'}} - 12 y = 0

y = c_{1} e^{\frac{( - 3 + 57 ) t}{2}} + c_{2} e^{\frac{( - 3 - 57 ) t}{2}}

Solution steps

y^{''} (t) + 3 y^{'} (t) - 12 y = 0

Solve linear ODE:

y = c_{1} e^{\frac{( - 3 + 57 ) t}{2}} + c_{2} e^{\frac{( - 3 - 57 ) t}{2}}

y = c_{1} e^{\frac{( - 3 + 57 ) t}{2}} + c_{2} e^{\frac{( - 3 - 57 ) t}{2}}

y = \frac{- 13}{3 x}

\int x sin (x^{\frac{3}{2}} + 1) d x

\frac{1}{x + 3}

\frac{d}{d x} (x (x^{3} - 5 x^{2} + 1))

\frac{\partial}{\partial x} (x y^{3} - x^{2} y)

What is the solution for y^{''}+3y^'-12y=0 ?
The solution for y^{''}+3y^'-12y=0 is y=c_{1}e^{((-3+sqrt(57))t)/2}+c_{2}e^{((-3-sqrt(57))t)/2}