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 = 2.21456 (sec), leaf count = 0 , could not solve
DSolve[x*Derivative[1][y][x] == Sin[x - y[x]], y[x], x]
Maple ✗
cpu = 4.735 (sec), leaf count = 0 , could not solve
dsolve(x*diff(y(x),x) = sin(x-y(x)), y(x))
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))
Maple raw output
dsolve(x*diff(y(x),x) = sin(x-y(x)), y(x))