ODE
\[ y''(x)+y(x)=e^{-x} \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.174153 (sec), leaf count = 25
\[\left \{\left \{y(x)\to \frac {e^{-x}}{2}+c_1 \cos (x)+c_2 \sin (x)\right \}\right \}\]
Maple ✓
cpu = 0.011 (sec), leaf count = 19
\[\left [y \left (x \right ) = \sin \left (x \right ) \textit {\_C2} +\textit {\_C1} \cos \left (x \right )+\frac {{\mathrm e}^{-x}}{2}\right ]\] Mathematica raw input
DSolve[y[x] + y''[x] == E^(-x),y[x],x]
Mathematica raw output
{{y[x] -> 1/(2*E^x) + C[1]*Cos[x] + C[2]*Sin[x]}}
Maple raw input
dsolve(diff(diff(y(x),x),x)+y(x) = exp(-x), y(x))
Maple raw output
[y(x) = sin(x)*_C2+_C1*cos(x)+1/2*exp(-x)]