ODE
\[ 2 y'''(x)+y'''''(x)+y'(x)=a x+b \cos (x)+c \sin (x) \] ODE Classification
[[_high_order, _missing_y]]
Book solution method
TO DO
Mathematica ✓
cpu = 1.1204 (sec), leaf count = 80
\[\left \{\left \{y(x)\to \frac {1}{16} \left (8 a x^2+\cos (x) \left (c \left (2 x^2-9\right )-2 (5 b x+8 (c_4 x-c_2+c_3))\right )+\sin (x) \left (b \left (13-2 x^2\right )-6 c x+16 (c_2 x+c_1+c_4)\right )\right )+c_5\right \}\right \}\]
Maple ✓
cpu = 2.582 (sec), leaf count = 78
\[\left [y \left (x \right ) = \frac {a \,x^{2}}{2}-\textit {\_C2} \cos \left (x \right )+\sin \left (x \right ) \textit {\_C1} -\cos \left (x \right ) \textit {\_C3} x +\sin \left (x \right ) \textit {\_C3} +\textit {\_C4} \sin \left (x \right ) x +\cos \left (x \right ) \textit {\_C4} +\frac {3 b \sin \left (x \right )}{4}-\frac {3 c \cos \left (x \right )}{4}-\frac {\sin \left (x \right ) c x}{2}-\frac {\cos \left (x \right ) b x}{2}-\frac {\sin \left (x \right ) b \,x^{2}}{8}+\frac {\cos \left (x \right ) c \,x^{2}}{8}+\textit {\_C5}\right ]\] Mathematica raw input
DSolve[y'[x] + 2*y'''[x] + y'''''[x] == a*x + b*Cos[x] + c*Sin[x],y[x],x]
Mathematica raw output
{{y[x] -> C[5] + (8*a*x^2 + (c*(-9 + 2*x^2) - 2*(5*b*x + 8*(-C[2] + C[3] + x*C[4])))*Cos[x] + (-6*c*x + b*(13 - 2*x^2) + 16*(C[1] + x*C[2] + C[4]))*Sin[x])/16}}
Maple raw input
dsolve(diff(diff(diff(diff(diff(y(x),x),x),x),x),x)+2*diff(diff(diff(y(x),x),x),x)+diff(y(x),x) = a*x+b*cos(x)+c*sin(x), y(x))
Maple raw output
[y(x) = 1/2*a*x^2-_C2*cos(x)+sin(x)*_C1-cos(x)*_C3*x+sin(x)*_C3+_C4*sin(x)*x+cos(x)*_C4+3/4*b*sin(x)-3/4*c*cos(x)-1/2*sin(x)*c*x-1/2*cos(x)*b*x-1/8*sin(x)*b*x^2+1/8*cos(x)*c*x^2+_C5]