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 = 0.6732 (sec), leaf count = 80
\[\left \{\left \{y(x)\to \frac {a x^2}{2}+\sin (x) \left (-\frac {b x^2}{8}+\frac {13 b}{16}-\frac {3 c x}{8}+c_2 x+c_1+c_4\right )+\cos (x) \left (-\frac {5 b x}{8}+\frac {1}{16} c \left (2 x^2-9\right )-c_4 x+c_2-c_3\right )+c_5\right \}\right \}\]
Maple ✓
cpu = 0.412 (sec), leaf count = 69
\[ \left \{ y \left ( x \right ) ={\frac { \left ( c{x}^{2}+ \left ( -4\,b-8\,{\it \_C4} \right ) x-6\,c-8\,{\it \_C2}+8\,{\it \_C3} \right ) \cos \left ( x \right ) }{8}}+{\frac { \left ( -b{x}^{2}+ \left ( -4\,c+8\,{\it \_C3} \right ) x+6\,b+8\,{\it \_C1}+8\,{\it \_C4} \right ) \sin \left ( x \right ) }{8}}+{\frac {a{x}^{2}}{2}}+{\it \_C5} \right \} \] 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] -> (a*x^2)/2 + C[5] + ((-5*b*x)/8 + (c*(-9 + 2*x^2))/16 + C[2] - C[3] - x*C[4])*Cos[x] + ((13*b)/16 - (3*c*x)/8 - (b*x^2)/8 + C[1] + x*C[2] + C[4])*Sin[x]}}
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),'implicit')
Maple raw output
y(x) = 1/8*(c*x^2+(-4*b-8*_C4)*x-6*c-8*_C2+8*_C3)*cos(x)+1/8*(-b*x^2+(-4*c+8*_C3)*x+6*b+8*_C1+8*_C4)*sin(x)+1/2*a*x^2+_C5