4.11.34 \((a+x (y(x)+x)) y'(x)=b y(x) (y(x)+x)\)

ODE
\[ (a+x (y(x)+x)) y'(x)=b y(x) (y(x)+x) \] ODE Classification

[_rational, [_Abel, `2nd type``class B`]]

Book solution method
Homogeneous equation, special

Mathematica
cpu = 74.1937 (sec), leaf count = 0 , could not solve

DSolve[(a + x*(x + y[x]))*Derivative[1][y][x] == b*y[x]*(x + y[x]), y[x], x]

Maple
cpu = 5.767 (sec), leaf count = 0 , could not solve

dsolve((a+x*(x+y(x)))*diff(y(x),x) = b*(x+y(x))*y(x), y(x),'implicit')

Mathematica raw input

DSolve[(a + x*(x + y[x]))*y'[x] == b*y[x]*(x + y[x]),y[x],x]

Mathematica raw output

DSolve[(a + x*(x + y[x]))*Derivative[1][y][x] == b*y[x]*(x + y[x]), y[x], x]

Maple raw input

dsolve((a+x*(x+y(x)))*diff(y(x),x) = b*(x+y(x))*y(x), y(x),'implicit')

Maple raw output

dsolve((a+x*(x+y(x)))*diff(y(x),x) = b*(x+y(x))*y(x), y(x),'implicit')