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

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

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

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

y = 3 x^{2} ln (x) - 2 x + c_{1} x^{2}

Solution steps

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

Solve linear ODE:

y = 3 x^{2} ln (x) - 2 x + c_{1} x^{2}

y = 3 x^{2} ln (x) - 2 x + c_{1} x^{2}

\frac{\partial}{\partial y} (arctan (y^{3} x))

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

y = sin (arccos (t))

\frac{d}{d x} (\frac{15}{x ^{2}})

\int_{0}^{12} \frac{1}{36 - x ^{2}} d x

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