15.18.10 problem 10

Internal problem ID [3253]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 35, page 157
Problem number : 10
Date solved : Sunday, March 30, 2025 at 01:25:11 AM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 23

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

\[ y = -\frac {x^{2} \ln \left (x \right )}{2}+\frac {\left (2 c_1 +1\right ) x^{2}}{4}+c_2 \]

✓ Mathematica. Time used: 0.034 (sec). Leaf size: 30

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

\[ y(x)\to -\frac {1}{2} x^2 \log (x)+\frac {1}{4} (1+2 c_1) x^2+c_2 \]

✓ Sympy. Time used: 0.196 (sec). Leaf size: 17

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

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