What is the solution for y^{'''}+5y^{''}-14=0 ?

The solution for y^{'''}+5y^{''}-14=0 is y=c_{1}e^{-5t}+c_{2}+c_{3}t+(7t^2)/5

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y^{'''}+5y^{''}-14=0

y^{^{'''}} + 5 y^{^{''}} - 14 = 0

y = c_{1} e^{- 5 t} + c_{2} + c_{3} t + \frac{7 t ^{2}}{5}

Solution steps

y^{'''} (t) + 5 y^{''} (t) - 14 = 0

Solve linear ODE:

y = c_{1} e^{- 5 t} + c_{2} + c_{3} t + \frac{7 t ^{2}}{5}

y = c_{1} e^{- 5 t} + c_{2} + c_{3} t + \frac{7 t ^{2}}{5}

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

x^{^{''}} - 6 x^{^{'}} + 9 x = e^{3 t}

y^{^{''}} + 2 y^{^{'}} + 5 y = e^{- x} cos (2 x)

y^{^{''}} + 100 y^{^{'}} + 2500 y = 30, y (0) = 0, y^{^{'}} (0) = 2

\frac{d ^{2} x}{d t ^{2}} + x = 6 cos (2 t), x (0) = 3

What is the solution for y^{'''}+5y^{''}-14=0 ?
The solution for y^{'''}+5y^{''}-14=0 is y=c_{1}e^{-5t}+c_{2}+c_{3}t+(7t^2)/5