# How you solve this? x^2y'+x^2y^2-3xy+3=0 with solution y_1=3/x

Apr 11, 2018

$y = \frac{{C}_{1} + 3 {C}_{2} {x}^{2}}{{C}_{1} x + {C}_{2} {x}^{3}}$

#### Explanation:

Making the substitution

$y = \frac{\xi '}{\xi}$ we have after substitution

${x}^{2} \xi ' ' - 3 x \xi ' + 3 \xi = 0$

this is linear differential equation with solution

$\xi \left(x\right) = {C}_{1} x + {C}_{2} {x}^{3}$ then

$y = \frac{{C}_{1} + 3 {C}_{2} {x}^{2}}{{C}_{1} x + {C}_{2} {x}^{3}}$