What is the solution for y^{'''}+3y^{''}-y^'-3y=3x-14 ?

The solution for y^{'''}+3y^{''}-y^'-3y=3x-14 is y=c_{1}e^{-3x}+c_{2}e^{-x}+c_{3}e^x-x+5

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y^{'''}+3y^{''}-y^'-3y=3x-14

y^{^{'''}} + 3 y^{^{''}} - y^{^{'}} - 3 y = 3 x - 14

y = c_{1} e^{- 3 x} + c_{2} e^{- x} + c_{3} e^{x} - x + 5

Solution steps

y^{'''} (x) + 3 y^{''} (x) - y^{'} (x) - 3 y = 3 x - 14

Solve linear ODE:

y = c_{1} e^{- 3 x} + c_{2} e^{- x} + c_{3} e^{x} - x + 5

y = c_{1} e^{- 3 x} + c_{2} e^{- x} + c_{3} e^{x} - x + 5

y^{^{''}} - 16 y^{^{'}} + 64 y = - \frac{2}{3 x} e^{8 x}

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + 4 y = 4 (x - 1)

y^{^{''}} - 6 y^{^{'}} - 3 + cos (x) = 0

\frac{d ^{2} y}{d x ^{2}} + y - 1 = 0, y (1) = 0

y^{^{''}} - 4 y = (x^{2} - 5) sin (2 x)

What is the solution for y^{'''}+3y^{''}-y^'-3y=3x-14 ?
The solution for y^{'''}+3y^{''}-y^'-3y=3x-14 is y=c_{1}e^{-3x}+c_{2}e^{-x}+c_{3}e^x-x+5