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}}

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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}