66.2.39 problem Problem 54

Internal problem ID [13938]
Book : Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS, MOSCOW, Third printing 1977.
Section : Chapter 2, DIFFERENTIAL EQUATIONS OF THE SECOND ORDER AND HIGHER. Problems page 172
Problem number : Problem 54
Date solved : Tuesday, January 28, 2025 at 06:09:12 AM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\left (6\right )}+2 y^{\prime \prime \prime \prime }+y^{\prime \prime }&=x +{\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 46

dsolve(diff(y(x),x$6)+2*diff(y(x),x$4)+diff(y(x),x$2)=x+exp(x),y(x), singsol=all)
 

\[ y = \left (-c_{3} x -2 c_4 -c_{1} \right ) \cos \left (x \right )+\left (-c_4 x -c_{2} +2 c_{3} \right ) \sin \left (x \right )+\frac {x^{3}}{6}+x c_5 +c_6 +\frac {{\mathrm e}^{x}}{4} \]

✓ Solution by Mathematica

Time used: 0.346 (sec). Leaf size: 58

DSolve[D[y[x],{x,6}]+2*D[y[x],{x,4}]+D[y[x],{x,2}]==x+Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x^3}{6}+\frac {e^x}{4}+c_6 x-(c_2 x+c_1+2 c_4) \cos (x)+(-c_4 x+2 c_2-c_3) \sin (x)+c_5 \]