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))