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

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

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(dy)/(dx)-y/x =2x^2ln(x)

\frac{d y}{d x} - \frac{y}{x} = 2 x^{2} ln (x)

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

Solution steps

\frac{d y}{d x} - \frac{y}{x} = 2 x^{2} ln (x)

Solve linear ODE:

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

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

x \to 1 lim (4 x^{2} - 2 x + 5)

\frac{d}{d x} (\frac{1 + \frac{1}{x}}{1 - \frac{1}{x}})

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

x \to 3 lim (\frac{x ^{2} + 3}{x - 1})

\int x^{2} x^{3} + 31 d x

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