75.14.14 problem 340

Internal problem ID [16928]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 14. Differential equations admitting of depression of their order. Exercises page 107
Problem number : 340
Date solved : Tuesday, January 28, 2025 at 09:41:09 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: 0.004 (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: 0.026 (sec). Leaf size: 21

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

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