ODE No. 917

y(x)=y(x)(xlog2(y(x))+2xlog(x)log(y(x))+xlog(y(x))+log(y(x))x+xlog2(x)+xlog(x)+log(x)1)x(x+1) Mathematica : cpu = 0.199566 (sec), leaf count = 28

DSolve[Derivative[1][y][x] == ((-1 - x + Log[x] + x*Log[x] + x*Log[x]^2 + Log[y[x]] + x*Log[y[x]] + 2*x*Log[x]*Log[y[x]] + x*Log[y[x]]^2)*y[x])/(x*(1 + x)),y[x],x]
 

{{y(x)exxlog(x+1)c1x}} Maple : cpu = 0.202 (sec), leaf count = 38

dsolve(diff(y(x),x) = y(x)*(x*ln(x)+ln(x)+ln(y(x))*x+ln(y(x))-x-1+x*ln(x)^2+2*x*ln(y(x))*ln(x)+x*ln(y(x))^2)/x/(1+x),y(x))
 

y(x)=eln(1+x)ln(x)+(x+c1)ln(x)xln(1+x)c1+x