What is the solution for y^{''}+7y^'-12y=0 ?

The solution for y^{''}+7y^'-12y=0 is y=c_{1}e^{((-7+sqrt(97))t)/2}+c_{2}e^{((-7-sqrt(97))t)/2}

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y^{''}+7y^'-12y=0

y^{^{''}} + 7 y^{^{'}} - 12 y = 0

y = c_{1} e^{\frac{( - 7 + 97 ) t}{2}} + c_{2} e^{\frac{( - 7 - 97 ) t}{2}}

Solution steps

y^{''} (t) + 7 y^{'} (t) - 12 y = 0

Solve linear ODE:

y = c_{1} e^{\frac{( - 7 + 97 ) t}{2}} + c_{2} e^{\frac{( - 7 - 97 ) t}{2}}

y = c_{1} e^{\frac{( - 7 + 97 ) t}{2}} + c_{2} e^{\frac{( - 7 - 97 ) t}{2}}

\frac{d ^{2} y}{d x ^{2}} + 3 \frac{d y}{d x} + 8 y = 0

y^{^{''}} + y = 0, y (0) = 3, y (0) = 30

y^{^{''}} + 4^{2} y = 0

3 \frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} + y = 0

y^{^{''}} - y^{^{'}} + 4 y = 0

What is the solution for y^{''}+7y^'-12y=0 ?
The solution for y^{''}+7y^'-12y=0 is y=c_{1}e^{((-7+sqrt(97))t)/2}+c_{2}e^{((-7-sqrt(97))t)/2}