What is the solution for x^2(d^2y)/(dx^2)+x*(dy)/(dx)-y=1 ?

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

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x^2(d^2y)/(dx^2)+x*(dy)/(dx)-y=1

x^{2} \frac{d ^{2} y}{d x ^{2}} + x \cdot \frac{d y}{d x} - y = 1

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

Solution steps

x^{2} \frac{d ^{2} y}{d x ^{2}} + x \cdot \frac{d y}{d x} - y = 1

Solve linear ODE:

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

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

\int y^{2} (9 - y^{3})^{\frac{2}{3}} d y

\int 12 (2 x + 7) (x + 1)^{2} d x

f (x) = 2 e^{2 x}

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

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