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 = 67.5389 (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 = 4.998 (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))
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))
Maple raw output
dsolve((a+x*(x+y(x)))*diff(y(x),x) = b*(x+y(x))*y(x), y(x))