4.5.10 \(x y'(x)=\sin (x-y(x))\)

ODE
\[ x y'(x)=\sin (x-y(x)) \] ODE Classification

[`y=_G(x,y')`]

Book solution method
Change of Variable, new dependent variable

Mathematica
cpu = 2.94972 (sec), leaf count = 0 , could not solve

DSolve[x*Derivative[1][y][x] == Sin[x - y[x]], y[x], x]

Maple
cpu = 1.532 (sec), leaf count = 0 , could not solve

dsolve(x*diff(y(x),x) = sin(x-y(x)), y(x),'implicit')

Mathematica raw input

DSolve[x*y'[x] == Sin[x - y[x]],y[x],x]

Mathematica raw output

DSolve[x*Derivative[1][y][x] == Sin[x - y[x]], y[x], x]

Maple raw input

dsolve(x*diff(y(x),x) = sin(x-y(x)), y(x),'implicit')

Maple raw output

dsolve(x*diff(y(x),x) = sin(x-y(x)), y(x),'implicit')