4.11.27 \(x (a+y(x)) y'(x)+b x+c y(x)=0\)

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 = 7.59793 (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 = 2.755 (sec), leaf count = 0 , could not solve

dsolve(x*(a+y(x))*diff(y(x),x)+b*x+c*y(x) = 0, y(x),'implicit')

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),'implicit')

Maple raw output

dsolve(x*(a+y(x))*diff(y(x),x)+b*x+c*y(x) = 0, y(x),'implicit')