66.2.38 problem Problem 53

Internal problem ID [13937]
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 53
Date solved : Tuesday, January 28, 2025 at 06:09:11 AM
CAS classification : [[_high_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 65

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

\[ y = {\mathrm e}^{-x} \left (\left (c_{3} {\mathrm e}^{\frac {x}{2}}+c_5 \,{\mathrm e}^{\frac {3 x}{2}}\right ) \cos \left (\frac {\sqrt {3}\, x}{2}\right )+\left ({\mathrm e}^{\frac {x}{2}} c_4 +c_6 \,{\mathrm e}^{\frac {3 x}{2}}\right ) \sin \left (\frac {\sqrt {3}\, x}{2}\right )+{\mathrm e}^{2 x} c_{1} +\frac {{\mathrm e}^{3 x}}{63}+c_{2} \right ) \]

✓ Solution by Mathematica

Time used: 0.419 (sec). Leaf size: 85

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

\[ y(x)\to \frac {e^{2 x}}{63}+c_1 e^x+c_4 e^{-x}+e^{-x/2} \left (c_2 e^x+c_3\right ) \cos \left (\frac {\sqrt {3} x}{2}\right )+e^{-x/2} \left (c_6 e^x+c_5\right ) \sin \left (\frac {\sqrt {3} x}{2}\right ) \]