What is the solution for (d^2y)/(dx^2)-5(dy)/(dx)-14y=7+4x ?

The solution for (d^2y)/(dx^2)-5(dy)/(dx)-14y=7+4x is y=c_{1}e^{7x}+c_{2}e^{-2x}-(2x)/7-39/98

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(d^2y)/(dx^2)-5(dy)/(dx)-14y=7+4x

\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} - 14 y = 7 + 4 x

y = c_{1} e^{7 x} + c_{2} e^{- 2 x} - \frac{2 x}{7} - \frac{39}{98}

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} - 14 y = 7 + 4 x

Solve linear ODE:

y = c_{1} e^{7 x} + c_{2} e^{- 2 x} - \frac{2 x}{7} - \frac{39}{98}

y = c_{1} e^{7 x} + c_{2} e^{- 2 x} - \frac{2 x}{7} - \frac{39}{98}

y^{^{''}} - 3 y + 2 y = sin (e^{- x})

y^{^{'''}} + 16 y^{^{'}} = t

y^{^{''}} + 3 y^{^{'}} + 2 y = \frac{x}{e ^{x}} + \frac{x ^{2}}{e ^{2 x}}

y^{^{''}} + 2 y^{^{'}} + y = 12 e^{- x}

y^{^{''''}} - 5 y^{^{''}} + 4 = 0

What is the solution for (d^2y)/(dx^2)-5(dy)/(dx)-14y=7+4x ?
The solution for (d^2y)/(dx^2)-5(dy)/(dx)-14y=7+4x is y=c_{1}e^{7x}+c_{2}e^{-2x}-(2x)/7-39/98