What is the solution for y^{''}+7y^'-10y=0 ?

The solution for y^{''}+7y^'-10y=0 is y=c_{1}e^{((-7+sqrt(89))t)/2}+c_{2}e^{((-7-sqrt(89))t)/2}

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y^{''}+7y^'-10y=0

y^{^{''}} + 7 y^{^{'}} - 10 y = 0

y = c_{1} e^{\frac{( - 7 + 89 ) t}{2}} + c_{2} e^{\frac{( - 7 - 89 ) t}{2}}

Solution steps

y^{''} (t) + 7 y^{'} (t) - 10 y = 0

Solve linear ODE:

y = c_{1} e^{\frac{( - 7 + 89 ) t}{2}} + c_{2} e^{\frac{( - 7 - 89 ) t}{2}}

y = c_{1} e^{\frac{( - 7 + 89 ) t}{2}} + c_{2} e^{\frac{( - 7 - 89 ) t}{2}}

64 y^{^{''}} + 48 y^{^{'}} + 9 y = 0

x^{^{''}} + 2 x^{^{'}} + 2 x = 0, x (0) = 1, x^{^{'}} (0) = 0

y^{^{'''}} + 5 y^{^{''}} + 4 y^{^{'}} = 0

y^{^{''}} + 6 y^{^{'}} + 25 y = 0, y (0) = 4, y^{^{'}} (0) = - 11

64 y^{^{''}} - 81 y = 0

What is the solution for y^{''}+7y^'-10y=0 ?
The solution for y^{''}+7y^'-10y=0 is y=c_{1}e^{((-7+sqrt(89))t)/2}+c_{2}e^{((-7-sqrt(89))t)/2}