48.4.12 problem Problem 3.19

Internal problem ID [7554]
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
Date solved : Monday, January 27, 2025 at 03:05:44 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} a^{2} y^{\prime \prime \prime \prime }&=y^{\prime \prime } \end{align*}

✓ 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)
 

\[ y = c_{1} +c_{2} x +c_3 \,{\mathrm e}^{-\frac {x}{a}}+c_4 \,{\mathrm e}^{\frac {x}{a}} \]

✓ Solution by Mathematica

Time used: 0.077 (sec). Leaf size: 38

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

\[ y(x)\to a^2 e^{-\frac {x}{a}} \left (c_1 e^{\frac {2 x}{a}}+c_2\right )+c_4 x+c_3 \]