ODE
\[ 1-y'(x)=y(x)+x \] ODE Classification
[[_linear, `class A`]]
Book solution method
Homogeneous equation
Mathematica ✓
cpu = 0.00627231 (sec), leaf count = 18
\[\left \{\left \{y(x)\to c_1 e^{-x}-x+2\right \}\right \}\]
Maple ✓
cpu = 0.007 (sec), leaf count = 15
\[ \left \{ y \left ( x \right ) =-x+2+{{\rm e}^{-x}}{\it \_C1} \right \} \] Mathematica raw input
DSolve[1 - y'[x] == x + y[x],y[x],x]
Mathematica raw output
{{y[x] -> 2 - x + C[1]/E^x}}
Maple raw input
dsolve(1-diff(y(x),x) = x+y(x), y(x),'implicit')
Maple raw output
y(x) = -x+2+exp(-x)*_C1