What is the solution for (d^2y)/(dx^2)+4(dy)/(dx)+3y=6x^2+19x+5 ?

The solution for (d^2y)/(dx^2)+4(dy)/(dx)+3y=6x^2+19x+5 is y=c_{1}e^{-x}+c_{2}e^{-3x}+2x^2+x-1

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(d^2y)/(dx^2)+4(dy)/(dx)+3y=6x^2+19x+5

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 3 y = 6 x^{2} + 19 x + 5

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 3 y = 6 x^{2} + 19 x + 5

Solve linear ODE:

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

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

What is the solution for (d^2y)/(dx^2)+4(dy)/(dx)+3y=6x^2+19x+5 ?
The solution for (d^2y)/(dx^2)+4(dy)/(dx)+3y=6x^2+19x+5 is y=c_{1}e^{-x}+c_{2}e^{-3x}+2x^2+x-1