What is the solution for y^{'''}-5y^{''}+6y^'=7+7 ?

The solution for y^{'''}-5y^{''}+6y^'=7+7 is y=c_{1}+c_{2}e^{2t}+c_{3}e^{3t}+(7t)/3

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y^{'''}-5y^{''}+6y^'=7+7

y^{^{'''}} - 5 y^{^{''}} + 6 y^{^{'}} = 7 + 7

y = c_{1} + c_{2} e^{2 t} + c_{3} e^{3 t} + \frac{7 t}{3}

Solution steps

y^{'''} (t) - 5 y^{''} (t) + 6 y^{'} (t) = 7 + 7

Solve linear ODE:

y = c_{1} + c_{2} e^{2 t} + c_{3} e^{3 t} + \frac{7 t}{3}

y = c_{1} + c_{2} e^{2 t} + c_{3} e^{3 t} + \frac{7 t}{3}

x^{^{''}} - a x = t

y^{^{''}} + 64 y = 16 sin (4 t), y (0) = \frac{1}{2}, y^{^{'}} (0) = 0

y^{^{''}} - 4 y^{^{'}} + 4 y = 5 e^{2 x}

y^{^{''}} + 3 y = 2 x

y^{^{''}} + 16 y = cos (4 t), y (0) = 0, y^{^{'}} (0) = 1

What is the solution for y^{'''}-5y^{''}+6y^'=7+7 ?
The solution for y^{'''}-5y^{''}+6y^'=7+7 is y=c_{1}+c_{2}e^{2t}+c_{3}e^{3t}+(7t)/3