60.6.2 problem 1579

Internal problem ID [11578]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 5, linear fifth and higher order
Problem number : 1579
Date solved : Monday, January 27, 2025 at 11:23:37 PM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\left (5\right )}+2 y^{\prime \prime \prime }+y^{\prime }-a x -b \sin \left (x \right )-c \cos \left (x \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 69

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)
 

\[ y = \frac {\left (b \,x^{2}+\left (-4 c -8 c_4 \right ) x -6 b -8 c_{2} +8 c_3 \right ) \cos \left (x \right )}{8}+\frac {\left (-c \,x^{2}+\left (-4 b +8 c_3 \right ) x +6 c +8 c_{1} +8 c_4 \right ) \sin \left (x \right )}{8}+\frac {a \,x^{2}}{2}+c_5 \]

✓ Solution by Mathematica

Time used: 0.596 (sec). Leaf size: 200

DSolve[D[y[x],{x,5}]+2*D[y[x],{x,3}]+D[y[x],x]-a*x-b*Sin[x]-c*Cos[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \int _1^x\left (c_1 \cos (K[5])+c_2 K[5] \cos (K[5])+\int _1^{K[5]}\frac {1}{2} (\cos (K[1]) K[1]-\sin (K[1])) (c \cos (K[1])+a K[1]+b \sin (K[1]))dK[1] \cos (K[5])+K[5] \int _1^{K[5]}-\frac {1}{2} \cos (K[2]) (c \cos (K[2])+a K[2]+b \sin (K[2]))dK[2] \cos (K[5])+c_3 \sin (K[5])+c_4 K[5] \sin (K[5])+\sin (K[5]) \int _1^{K[5]}\frac {1}{2} (c \cos (K[3])+a K[3]+b \sin (K[3])) (\cos (K[3])+K[3] \sin (K[3]))dK[3]+K[5] \sin (K[5]) \int _1^{K[5]}-\frac {1}{2} \sin (K[4]) (c \cos (K[4])+a K[4]+b \sin (K[4]))dK[4]\right )dK[5]+c_5 \]