Internal problem ID [5133]
Book: THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T.
CHAU, CRC Press. Boca Raton, FL. 2018
Section: Chapter 3. Ordinary Differential Equations. Section 3.6 Summary and Problems. Page
218
Problem number: Problem 3.19.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
Solve \begin {gather*} \boxed {a^{2} y^{\prime \prime \prime \prime }-y^{\prime \prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 26
dsolve(a^2*diff(y(x),x$4)=diff(y(x),x$2),y(x), singsol=all)
\[ y \relax (x ) = c_{1}+c_{2} x +c_{3} {\mathrm e}^{\frac {x}{a}}+c_{4} {\mathrm e}^{-\frac {x}{a}} \]
✓ Solution by Mathematica
Time used: 0.035 (sec). Leaf size: 38
DSolve[a^2*y''''[x]==y''[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to a^2 e^{-\frac {x}{a}} \left (c_1 e^{\frac {2 x}{a}}+c_2\right )+c_4 x+c_3 \\ \end{align*}