76.24.13 problem 15

Internal problem ID [17812]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 6. Systems of First Order Linear Equations. Section 6.2 (Basic Theory of First Order Linear Systems). Problems at page 398
Problem number : 15
Date solved : Tuesday, January 28, 2025 at 11:03:19 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} x y^{\prime \prime \prime }-y^{\prime \prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 14

dsolve(x*diff(y(x),x$3)-diff(y(x),x$2)=0,y(x), singsol=all)
 

\[ y = c_{2} x^{3}+c_{3} x +c_{1} \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 21

DSolve[x*D[y[x],{x,3}]-D[y[x],{x,2}]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_1 x^3}{6}+c_3 x+c_2 \]