ODE
\[ y''(x)+y(x)=e^x \sin (2 x) \] ODE Classification
[[_2nd_order, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.269575 (sec), leaf count = 37
\[\left \{\left \{y(x)\to -\frac {1}{5} e^x \cos (2 x)+c_2 \sin (x)+\cos (x) \left (-\frac {1}{5} e^x \sin (x)+c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.35 (sec), leaf count = 28
\[\left [y \left (x \right ) = \sin \left (x \right ) \textit {\_C2} +\textit {\_C1} \cos \left (x \right )-\frac {{\mathrm e}^{x} \left (2 \cos \left (2 x \right )+\sin \left (2 x \right )\right )}{10}\right ]\] Mathematica raw input
DSolve[y[x] + y''[x] == E^x*Sin[2*x],y[x],x]
Mathematica raw output
{{y[x] -> -1/5*(E^x*Cos[2*x]) + C[2]*Sin[x] + Cos[x]*(C[1] - (E^x*Sin[x])/5)}}
Maple raw input
dsolve(diff(diff(y(x),x),x)+y(x) = exp(x)*sin(2*x), y(x))
Maple raw output
[y(x) = sin(x)*_C2+_C1*cos(x)-1/10*exp(x)*(2*cos(2*x)+sin(2*x))]