What is the solution for 2(d^2y)/(dx^2)+11(dy)/(dx)-6y=8x ?

The solution for 2(d^2y)/(dx^2)+11(dy)/(dx)-6y=8x is y=c_{1}e^{x/2}+c_{2}e^{-6x}-(4x)/3-22/9

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2(d^2y)/(dx^2)+11(dy)/(dx)-6y=8x

2 \frac{d ^{2} y}{d x ^{2}} + 11 \frac{d y}{d x} - 6 y = 8 x

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{- 6 x} - \frac{4 x}{3} - \frac{22}{9}

Solution steps

2 \frac{d ^{2} y}{d x ^{2}} + 11 \frac{d y}{d x} - 6 y = 8 x

Solve linear ODE:

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{- 6 x} - \frac{4 x}{3} - \frac{22}{9}

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{- 6 x} - \frac{4 x}{3} - \frac{22}{9}

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

x \to 2 lim (x^{3} + 5 x^{2} - 7 x + 1)

\frac{d}{d x} (- \frac{25}{( 1 + 5 x ) ^{2}})

\frac{x}{5} + \frac{5}{x}

\int 6 x^{3} 3 x^{4} + 2 d x

What is the solution for 2(d^2y)/(dx^2)+11(dy)/(dx)-6y=8x ?
The solution for 2(d^2y)/(dx^2)+11(dy)/(dx)-6y=8x is y=c_{1}e^{x/2}+c_{2}e^{-6x}-(4x)/3-22/9