4.9.41 \(1-y'(x)=y(x)+x\)

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

\[ \left \{ y \relax (x ) =-x+2+{{\rm e}^{-x}}{\it \_C1} \right \} \] 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