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

The solution for (dy)/(dx)=3y+x^2+2 is y=-(x^2)/3-(2x)/9-20/27+c_{1}e^{3x}

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(dy)/(dx)=3y+x^2+2

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

y = - \frac{x ^{2}}{3} - \frac{2 x}{9} - \frac{20}{27} + c_{1} e^{3 x}

Solution steps

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

Solve linear ODE:

y = - \frac{x ^{2}}{3} - \frac{2 x}{9} - \frac{20}{27} + c_{1} e^{3 x}

y = - \frac{x ^{2}}{3} - \frac{2 x}{9} - \frac{20}{27} + c_{1} e^{3 x}

\int \frac{- 1}{x - 1} d x

f (x) = - 4

\frac{\partial}{\partial x} (e^{- s i n^{2} (x)} (x + c))

\int x x^{\frac{3}{2} - 1} d x

\frac{d}{d x} ((x + 6)^{\frac{2}{3}})

What is the solution for (dy)/(dx)=3y+x^2+2 ?
The solution for (dy)/(dx)=3y+x^2+2 is y=-(x^2)/3-(2x)/9-20/27+c_{1}e^{3x}