What is the solution for (dy)/(dx)=2y+x^2e^{2x}+5 ?

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

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(dy)/(dx)=2y+x^2e^{2x}+5

\frac{d y}{d x} = 2 y + x^{2} e^{2 x} + 5

y = \frac{x ^{3}}{3 e ^{- 2 x}} - \frac{5}{2} + c_{1} e^{2 x}

Solution steps

\frac{d y}{d x} = 2 y + x^{2} e^{2 x} + 5

Solve linear ODE:

y = \frac{x ^{3}}{3 e ^{- 2 x}} - \frac{5}{2} + c_{1} e^{2 x}

y = \frac{x ^{3}}{3 e ^{- 2 x}} - \frac{5}{2} + c_{1} e^{2 x}

x \to 0 lim (2400 x - 2 x^{2})

x \to 1 lim (\frac{x}{( x - 1 )})

y = 6 x^{3} - x^{2}

f (x) = 2 x^{3} + 3 x^{2} - 12 x + 6, at x = 0

e^{x} \cdot x

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