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

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

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y^'+y^{''}=y^{'''}

y^{^{'}} + y^{^{''}} = y^{^{'''}}

y = c_{1} + c_{2} e^{\frac{( 1 + 5 ) t}{2}} + c_{3} e^{\frac{( 1 - 5 ) t}{2}}

Solution steps

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

Solve linear ODE:

y = c_{1} + c_{2} e^{\frac{( 1 + 5 ) t}{2}} + c_{3} e^{\frac{( 1 - 5 ) t}{2}}

y = c_{1} + c_{2} e^{\frac{( 1 + 5 ) t}{2}} + c_{3} e^{\frac{( 1 - 5 ) t}{2}}

y^{^{''}} + 8 y^{^{'}} + 15 y = 0, y (0) = 2, y (1) = 0

y^{^{''}} + 9 y^{^{'}} - 9 y = 0

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

y^{^{''}} + 6 y - 2 y = 0, y (0) = 1, y^{^{'}} (0) = 2

y^{^{''}} - 11 y + 18 y = 0

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