What is the solution for x^3dy+xydx=x^2dy+2ydx ?

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

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x^3dy+xydx=x^2dy+2ydx

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

y = e^{\frac{2 + c _{1} x}{x}} - \frac{e ^{\frac{2 + c _{1} x}{x}}}{x}

Solution steps

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

Solve separable ODE:

y = e^{\frac{2 + c _{1} x}{x}} - \frac{e ^{\frac{2 + c _{1} x}{x}}}{x}

y = e^{\frac{2 + c _{1} x}{x}} - \frac{e ^{\frac{2 + c _{1} x}{x}}}{x}

\frac{\partial}{\partial x} (ln (\frac{2 x - 1}{x - 1}))

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2 x^{4} 25 - x^{2}

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