Internal problem ID [12174]
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.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime \prime }-16 y=x^{2}-{\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 53
dsolve(diff(y(x),x$4)-16*y(x)=x^2-exp(x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\left (\left (\left (-16 c_{1} +\frac {1}{4}\right ) \cos \left (2 x \right )+x^{2}-16 c_{4} \sin \left (2 x \right )\right ) {\mathrm e}^{2 x}-16 c_{3} {\mathrm e}^{4 x}-16 c_{2} -\frac {16 \,{\mathrm e}^{3 x}}{15}\right ) {\mathrm e}^{-2 x}}{16} \]
✓ Solution by Mathematica
Time used: 0.299 (sec). Leaf size: 50
DSolve[y''''[x]-16*y[x]==x^2-Exp[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {x^2}{16}+\frac {e^x}{15}+c_1 e^{2 x}+c_3 e^{-2 x}+c_2 \cos (2 x)+c_4 \sin (2 x) \]