What is the solution for y^{''}+15y^'-56y=0 ?

The solution for y^{''}+15y^'-56y=0 is y=c_{1}e^{((-15+sqrt(449))t)/2}+c_{2}e^{((-15-sqrt(449))t)/2}

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y^{''}+15y^'-56y=0

y^{^{''}} + 15 y^{^{'}} - 56 y = 0

y = c_{1} e^{\frac{( - 15 + 449 ) t}{2}} + c_{2} e^{\frac{( - 15 - 449 ) t}{2}}

Solution steps

y^{''} (t) + 15 y^{'} (t) - 56 y = 0

Solve linear ODE:

y = c_{1} e^{\frac{( - 15 + 449 ) t}{2}} + c_{2} e^{\frac{( - 15 - 449 ) t}{2}}

y = c_{1} e^{\frac{( - 15 + 449 ) t}{2}} + c_{2} e^{\frac{( - 15 - 449 ) t}{2}}

What is the solution for y^{''}+15y^'-56y=0 ?
The solution for y^{''}+15y^'-56y=0 is y=c_{1}e^{((-15+sqrt(449))t)/2}+c_{2}e^{((-15-sqrt(449))t)/2}