Internal problem ID [10826]
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]]
\[ \boxed {y^{\prime \prime \prime \prime }-16 y-x^{2}+{\mathrm e}^{x}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 65
dsolve(diff(y(x),x$4)-16*y(x)=x^2-exp(x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {{\mathrm e}^{-2 x} {\mathrm e}^{2 x} \cos \left (2 x \right )}{64}+\frac {{\mathrm e}^{-2 x} \left (-15 x^{2} {\mathrm e}^{2 x}+16 \,{\mathrm e}^{3 x}\right )}{240}+c_{1} \cos \left (2 x \right )+c_{2} {\mathrm e}^{-2 x}+c_{3} {\mathrm e}^{2 x}+c_{4} \sin \left (2 x \right ) \]
✓ Solution by Mathematica
Time used: 0.199 (sec). Leaf size: 50
DSolve[y''''[x]-16*y[x]==x^2-Exp[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} 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) \\ \end{align*}