ODE
\[ y''(x)+3 y'(x)+2 y(x)=e^x+\sin (x) \] ODE Classification
[[_2nd_order, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0181714 (sec), leaf count = 40
\[\left \{\left \{y(x)\to c_1 e^{-2 x}+c_2 e^{-x}+\frac {1}{30} \left (5 e^x+3 \sin (x)-9 \cos (x)\right )\right \}\right \}\]
Maple ✓
cpu = 0.051 (sec), leaf count = 30
\[ \left \{ y \left ( x \right ) =-{\frac {3\,\cos \left ( x \right ) }{10}}+{\frac {\sin \left ( x \right ) }{10}}+{\frac {{{\rm e}^{x}}}{6}}-{\it \_C1}\,{{\rm e}^{-2\,x}}+{{\rm e}^{-x}}{\it \_C2} \right \} \] Mathematica raw input
DSolve[2*y[x] + 3*y'[x] + y''[x] == E^x + Sin[x],y[x],x]
Mathematica raw output
{{y[x] -> C[1]/E^(2*x) + C[2]/E^x + (5*E^x - 9*Cos[x] + 3*Sin[x])/30}}
Maple raw input
dsolve(diff(diff(y(x),x),x)+3*diff(y(x),x)+2*y(x) = sin(x)+exp(x), y(x),'implicit')
Maple raw output
y(x) = -3/10*cos(x)+1/10*sin(x)+1/6*exp(x)-_C1*exp(-2*x)+exp(-x)*_C2