eq:x*'diff('diff(y,x),x)+(x+2)*'diff(y,x)-y;

y1:1+x/2;

substitute(y=y1,eq)$ ev(%,nouns)$ ratsimp(%);

y3:C*y1*log(x)+b0/x+b1+b2*x+b3*x^2+b4*x^3;

substitute(y=y3,eq)$ ev(%,nouns)$ res:expand(%);

makelist(coeff(res,x,k),k,-1,2);
solve(%,[C,b2,b3,b4]);

y2:2*y1*log(x)+1/x-5*x/2-x^2/6+x^3/72-x^4/720;

substitute(y=y2,eq)$ ev(%,nouns)$ expand(%);