ODE No. 919

y(x)=(y(x)+y(x)+x)y(x)3/2x33x2y(x)+3xy(x)2+xy(x)3/2y(x)3y(x)5/2+y(x)2 Mathematica : cpu = 0.302682 (sec), leaf count = 251

DSolve[Derivative[1][y][x] == ((x + Sqrt[y[x]] - y[x])*y[x]^(3/2))/(x^3 - 3*x^2*y[x] + x*y[x]^(3/2) + y[x]^2 + 3*x*y[x]^2 - y[x]^(5/2) - y[x]^3),y[x],x]
 

{{y(x)Root[#19c146#18c14x+#17(15c14x26c12)+#16(20c14x3+30c12x4+2c12)+#15(15c14x460c12x2+24x6c12x+9)+#14(6c14x5+60c12x360x2+6c12x236x6)+#13(c14x630c12x4+80x32c12x3+54x2+12x+1)+#12(6c12x560x436x36x2)+#1(24x5+9x4)4x6&,1]}} Maple : cpu = 0.195 (sec), leaf count = 82

dsolve(diff(y(x),x) = y(x)^(3/2)*(x-y(x)+y(x)^(1/2))/(y(x)^(3/2)*x-y(x)^(5/2)+y(x)^2+x^3-3*x^2*y(x)+3*x*y(x)^2-y(x)^3),y(x))
 

(x3c16x1)y(x)52+(3x2c1+3)y(x)72y(x)112c1+3y(x)32x2+3y(x)92c1x2y(x)(xy(x))3y(x)52(xy(x))3=0