What is the solution for 2(d^2y)/(dx^2)+4(dy)/(dx)-6y=14e^x ?

The solution for 2(d^2y)/(dx^2)+4(dy)/(dx)-6y=14e^x is y=c_{1}e^x+c_{2}e^{-3x}+(7e^xx)/4

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2(d^2y)/(dx^2)+4(dy)/(dx)-6y=14e^x

2 \frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} - 6 y = 14 e^{x}

y = c_{1} e^{x} + c_{2} e^{- 3 x} + \frac{7 e ^{x} x}{4}

Solution steps

2 \frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} - 6 y = 14 e^{x}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 3 x} + \frac{7 e ^{x} x}{4}

y = c_{1} e^{x} + c_{2} e^{- 3 x} + \frac{7 e ^{x} x}{4}

\frac{1}{4} y^{^{''}} + 2 y^{^{'}} + 40 y = - \frac{20}{3} t - \frac{4}{3}

y^{^{''}} + 2 y^{^{'}} + 2 y = 10 sin (2 t)

y^{^{''}} + 2 y^{^{'}} = 4 x

y^{^{''}} + 3 y = x^{3} - 1

y^{^{''}} - 8 y^{^{'}} + 16 y = 8 e^{2 t}, y (0) = 3, y^{^{'}} (0) = 2

What is the solution for 2(d^2y)/(dx^2)+4(dy)/(dx)-6y=14e^x ?
The solution for 2(d^2y)/(dx^2)+4(dy)/(dx)-6y=14e^x is y=c_{1}e^x+c_{2}e^{-3x}+(7e^xx)/4