What is the solution for (dy)/(dx)+3y=3x^2e^{-3x} ?

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

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(dy)/(dx)+3y=3x^2e^{-3x}

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

y = \frac{x ^{3}}{e ^{3 x}} + \frac{c _{1}}{e ^{3 x}}

Solution steps

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

Solve linear ODE:

y = \frac{x ^{3}}{e ^{3 x}} + \frac{c _{1}}{e ^{3 x}}

y = \frac{x ^{3}}{e ^{3 x}} + \frac{c _{1}}{e ^{3 x}}

\int \frac{18}{9 x ^{2} - x ^{4}} d x

x \to 0 - lim (e^{\frac{x}{x + 1}})

\int \frac{1 + x ^{2}}{x ^{2}} d x

\int \frac{x ^{3} + x}{( x ^{2} + 3 ) ( x ^{2} - 2 x + 3 )} d x

\int e^{2 x} 1 + e^{x} d x

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