Question Number 220964 by fantastic last updated on 21/May/25
![Find the general solution of the differential equation x^2 (d^3 y/dx^3 ) + x(d^2 y/dx^2 )−6(dy/dx)+6(y/x)=((x ln x+1)/x^2 ),[x>0]](https://www.tinkutara.com/question/Q220964.png)
$${Find}\:{the}\:{general}\:{solution}\:{of}\:{the}\:{differential}\:{equation} \\ $$$${x}^{\mathrm{2}} \:\frac{{d}^{\mathrm{3}} {y}}{{dx}^{\mathrm{3}} }\:+\:{x}\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }−\mathrm{6}\frac{{dy}}{{dx}}+\mathrm{6}\frac{{y}}{{x}}=\frac{{x}\:\mathrm{ln}\:{x}+\mathrm{1}}{{x}^{\mathrm{2}} },\left[{x}>\mathrm{0}\right] \\ $$