ODE
\[ x (a+y(x)) y'(x)+b x+c y(x)=0 \] ODE Classification
[_rational, [_Abel, `2nd type`, `class B`]]
Book solution method
Change of Variable, new independent variable
Mathematica ✗
cpu = 4.71405 (sec), leaf count = 0 , could not solve
DSolve[b*x + c*y[x] + x*(a + y[x])*Derivative[1][y][x] == 0, y[x], x]
Maple ✗
cpu = 2.343 (sec), leaf count = 0 , could not solve
dsolve(x*(a+y(x))*diff(y(x),x)+b*x+c*y(x) = 0, y(x))
Mathematica raw input
DSolve[b*x + c*y[x] + x*(a + y[x])*y'[x] == 0,y[x],x]
Mathematica raw output
DSolve[b*x + c*y[x] + x*(a + y[x])*Derivative[1][y][x] == 0, y[x], x]
Maple raw input
dsolve(x*(a+y(x))*diff(y(x),x)+b*x+c*y(x) = 0, y(x))
Maple raw output
dsolve(x*(a+y(x))*diff(y(x),x)+b*x+c*y(x) = 0, y(x))