What is the solution for xy^'+3y=8x^2-6x ?

The solution for xy^'+3y=8x^2-6x is y=(8x^2)/5-(3x)/2+(c_{1})/(x^3)

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xy^'+3y=8x^2-6x

x y^{^{'}} + 3 y = 8 x^{2} - 6 x

y = \frac{8 x ^{2}}{5} - \frac{3 x}{2} + \frac{c _{1}}{x ^{3}}

Solution steps

x y^{'} (x) + 3 y = 8 x^{2} - 6 x

Solve linear ODE:

y = \frac{8 x ^{2}}{5} - \frac{3 x}{2} + \frac{c _{1}}{x ^{3}}

y = \frac{8 x ^{2}}{5} - \frac{3 x}{2} + \frac{c _{1}}{x ^{3}}

\frac{d}{d x} (\frac{( x + 1 ) ^{2}}{1 + x ^{2}})

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

4 x + 12, 8 - x^{2}, x = - 2, x = 6

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

\int_{- \infty}^{16} r e^{\frac{r}{4}} d r

What is the solution for xy^'+3y=8x^2-6x ?
The solution for xy^'+3y=8x^2-6x is y=(8x^2)/5-(3x)/2+(c_{1})/(x^3)