What is the solution for y^{''}=3y^'+5y ?

The solution for y^{''}=3y^'+5y is y=c_{1}e^{((3+sqrt(29))t)/2}+c_{2}e^{((3-sqrt(29))t)/2}

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y^{''}=3y^'+5y

y^{^{''}} = 3 y^{^{'}} + 5 y

y = c_{1} e^{\frac{( 3 + 29 ) t}{2}} + c_{2} e^{\frac{( 3 - 29 ) t}{2}}

Solution steps

y^{''} (t) = 3 y^{'} (t) + 5 y

Solve linear ODE:

y = c_{1} e^{\frac{( 3 + 29 ) t}{2}} + c_{2} e^{\frac{( 3 - 29 ) t}{2}}

y = c_{1} e^{\frac{( 3 + 29 ) t}{2}} + c_{2} e^{\frac{( 3 - 29 ) t}{2}}

3 y^{^{''}} + 38 y^{^{'}} + 80 y = 0, y (0) = 3, y^{^{'}} (0) = 7

a x^{^{''}} + b x^{^{'}} + c x = 0

y^{^{''}} - 361 y = 0

3 y^{^{''}} - 2 y^{^{'}} + 6 y = 0

y^{^{'''}} + 36 y^{^{'}} = 0, y (0) = 1

What is the solution for y^{''}=3y^'+5y ?
The solution for y^{''}=3y^'+5y is y=c_{1}e^{((3+sqrt(29))t)/2}+c_{2}e^{((3-sqrt(29))t)/2}