What is the solution for 3y^{''}+11y^'+6y=3x^2+7x+3 ?

The solution for 3y^{''}+11y^'+6y=3x^2+7x+3 is y=c_{1}e^{-(2x)/3}+c_{2}e^{-3x}+(x^2)/2-(2x)/3+11/9

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3y^{''}+11y^'+6y=3x^2+7x+3

3 y^{^{''}} + 11 y^{^{'}} + 6 y = 3 x^{2} + 7 x + 3

y = c_{1} e^{- \frac{2 x}{3}} + c_{2} e^{- 3 x} + \frac{x ^{2}}{2} - \frac{2 x}{3} + \frac{11}{9}

Solution steps

3 y^{''} (x) + 11 y^{'} (x) + 6 y = 3 x^{2} + 7 x + 3

Solve linear ODE:

y = c_{1} e^{- \frac{2 x}{3}} + c_{2} e^{- 3 x} + \frac{x ^{2}}{2} - \frac{2 x}{3} + \frac{11}{9}

y = c_{1} e^{- \frac{2 x}{3}} + c_{2} e^{- 3 x} + \frac{x ^{2}}{2} - \frac{2 x}{3} + \frac{11}{9}

\int_{1}^{3} \frac{3 x ^{2} - 7}{x ^{3}} d x

\frac{d P}{d t} = k P^{1.01}, P (0) = 10

y^{^{''}} + 2 y^{^{'}} + 5 y = 6 sin (2 t)

\frac{d ^{2}}{d x ^{2}} (cos (5 x))

x \to 0 lim (\frac{a ^{x} - b ^{x}}{x})

What is the solution for 3y^{''}+11y^'+6y=3x^2+7x+3 ?
The solution for 3y^{''}+11y^'+6y=3x^2+7x+3 is y=c_{1}e^{-(2x)/3}+c_{2}e^{-3x}+(x^2)/2-(2x)/3+11/9