##### 4.15.21 $$y'(x) (\text {f1}(x,y(x))+x \text {f2}(x,y(x)))=y(x) \text {f2}(x,y(x))+\text {f3}(x,y(x))$$

ODE
$y'(x) (\text {f1}(x,y(x))+x \text {f2}(x,y(x)))=y(x) \text {f2}(x,y(x))+\text {f3}(x,y(x))$ ODE Classiﬁcation

[NONE]

Book solution method
Homogeneous equation, Darbooux type

Mathematica
cpu = 3.822 (sec), leaf count = 0 , could not solve

DSolve[(f1[x, y[x]] + x*f2[x, y[x]])*Derivative[1][y][x] == f3[x, y[x]] + f2[x, y[x]]*y[x], y[x], x]

Maple
cpu = 0.006 (sec), leaf count = 0 , could not solve

dsolve((f1(x,y(x))+x*f2(x,y(x)))*diff(y(x),x) = f3(x,y(x))+y(x)*f2(x,y(x)), y(x))

Mathematica raw input

DSolve[(f1[x, y[x]] + x*f2[x, y[x]])*y'[x] == f3[x, y[x]] + f2[x, y[x]]*y[x],y[x],x]

Mathematica raw output

DSolve[(f1[x, y[x]] + x*f2[x, y[x]])*Derivative[1][y][x] == f3[x, y[x]] + f2[x,
y[x]]*y[x], y[x], x]

Maple raw input

dsolve((f1(x,y(x))+x*f2(x,y(x)))*diff(y(x),x) = f3(x,y(x))+y(x)*f2(x,y(x)), y(x))

Maple raw output

dsolve((f1(x,y(x))+x*f2(x,y(x)))*diff(y(x),x) = f3(x,y(x))+y(x)*f2(x,y(x)), y(x)
)