69.14.6 problem 332

Internal problem ID [18207]
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 : Thursday, October 02, 2025 at 03:09:04 PM
CAS classification : [[_2nd_order, _missing_y]]

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

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

ode:=x*diff(diff(y(x),x),x) = diff(y(x),x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_2 \,x^{2}+c_1 \]

✓ Mathematica. Time used: 0.006 (sec). Leaf size: 17

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

\begin{align*} y(x)&\to \frac {c_1 x^2}{2}+c_2 \end{align*}

✓ Sympy. Time used: 0.068 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), (x, 2)) - Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} x^{2} \]