66.2.11 problem Problem 11

Internal problem ID [13910]
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 11
Date solved : Tuesday, January 28, 2025 at 06:08:16 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }-16 y&=x^{2}-{\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 53

dsolve(diff(y(x),x$4)-16*y(x)=x^2-exp(x),y(x), singsol=all)
 

\[ y = -\frac {\left (\left (\left (-16 c_{1} +\frac {1}{4}\right ) \cos \left (2 x \right )+x^{2}-16 c_4 \sin \left (2 x \right )\right ) {\mathrm e}^{2 x}-16 c_{3} {\mathrm e}^{4 x}-16 c_{2} -\frac {16 \,{\mathrm e}^{3 x}}{15}\right ) {\mathrm e}^{-2 x}}{16} \]

✓ Solution by Mathematica

Time used: 0.214 (sec). Leaf size: 50

DSolve[D[y[x],{x,4}]-16*y[x]==x^2-Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {x^2}{16}+\frac {e^x}{15}+c_1 e^{2 x}+c_3 e^{-2 x}+c_2 \cos (2 x)+c_4 \sin (2 x) \]