Internal problem ID [9911]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 5, linear fifth and higher order
Problem number: 1579.
ODE order: 5.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_y]]
\[ \boxed {y^{\left (5\right )}+2 y^{\prime \prime \prime }+y^{\prime }=a x +b \sin \left (x \right )+c \cos \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 78
dsolve(diff(y(x),x$5)+2*diff(y(x),x$3)+diff(y(x),x)-a*x-b*sin(x)-c*cos(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {a \,x^{2}}{2}+c_{1} \sin \left (x \right )-c_{2} \cos \left (x \right )+\frac {3 c \sin \left (x \right )}{4}-\frac {3 b \cos \left (x \right )}{4}-\frac {\sin \left (x \right ) x b}{2}+\sin \left (x \right ) c_{3} x +\cos \left (x \right ) c_{3} -\cos \left (x \right ) c_{4} x +\sin \left (x \right ) c_{4} -\frac {\sin \left (x \right ) c \,x^{2}}{8}-\frac {\cos \left (x \right ) c x}{2}+\frac {\cos \left (x \right ) b \,x^{2}}{8}+c_{5} \]
✓ Solution by Mathematica
Time used: 1.166 (sec). Leaf size: 80
DSolve[y'''''[x]+2*y'''[x]+y'[x]-a*x-b*Sin[x]-c*Cos[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{16} \left (8 a x^2+\cos (x) \left (b \left (2 x^2-9\right )-2 (5 c x+8 (c_4 x-c_2+c_3))\right )+\sin (x) \left (-6 b x+c \left (13-2 x^2\right )+16 (c_2 x+c_1+c_4)\right )\right )+c_5 \]