2.390   ODE No. 390

ay(x)y(x)bxc+y(x)2=0

Mathematica : cpu = 3.40758 (sec), leaf count = 161

DSolve[-c - b*x + a*y[x]*Derivative[1][y][x] + Derivative[1][y][x]^2 == 0,y[x],x]
 
Solve[{x=(alog(baK[1]2aK[1])(a)3/2cbaK[1]2bK[1])exp(b(log(K[1])blog(baK[1]2)2b))+c1exp(b(log(K[1])blog(baK[1]2)2b)),y(x)=bxaK[1]+cK[1]2aK[1]},{y(x),K[1]}]

Maple : cpu = 0.305 (sec), leaf count = 281

dsolve(diff(y(x),x)^2+a*y(x)*diff(y(x),x)-b*x-c = 0,y(x))
 
y(x)=2eRootOf(ac1be2_Ze2_Zabxe2_Z_Zbe2_Zac+ac1b2+ab2x_Zb2+abc)((e2RootOf(ac1be2_Ze2_Zabxe2_Z_Zbe2_Zac+ac1b2+ab2x_Zb2+abc)+b)2e2RootOf(ac1be2_Ze2_Zabxe2_Z_Zbe2_Zac+ac1b2+ab2x_Zb2+abc)4+a(bx+c))a3/2(e2RootOf(ac1be2_Ze2_Zabxe2_Z_Zbe2_Zac+ac1b2+ab2x_Zb2+abc)+b)