ODE
\[ y''(x)+y(x)=4 x \sin (x) \] ODE Classification
[[_2nd_order, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.170968 (sec), leaf count = 27
\[\left \{\left \{y(x)\to \left (-x^2+\frac {1}{2}+c_1\right ) \cos (x)+(x+c_2) \sin (x)\right \}\right \}\]
Maple ✓
cpu = 0.116 (sec), leaf count = 23
\[[y \left (x \right ) = \sin \left (x \right ) \textit {\_C2} +\textit {\_C1} \cos \left (x \right )+x \left (-x \cos \left (x \right )+\sin \left (x \right )\right )]\] Mathematica raw input
DSolve[y[x] + y''[x] == 4*x*Sin[x],y[x],x]
Mathematica raw output
{{y[x] -> (1/2 - x^2 + C[1])*Cos[x] + (x + C[2])*Sin[x]}}
Maple raw input
dsolve(diff(diff(y(x),x),x)+y(x) = 4*x*sin(x), y(x))
Maple raw output
[y(x) = sin(x)*_C2+_C1*cos(x)+x*(-x*cos(x)+sin(x))]