75.14.6 problem 332

Internal problem ID [16920]
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 : 332
Date solved : Tuesday, January 28, 2025 at 09:40:56 AM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 11

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

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

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 17

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

\[ y(x)\to \frac {c_1 x^2}{2}+c_2 \]