15.18.12 problem 12

Internal problem ID [3255]
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 : 12
Date solved : Sunday, March 30, 2025 at 01:25:15 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} x^{2} y^{\prime \prime }&=x y^{\prime }+1 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

ode:=x^2*diff(diff(y(x),x),x) = x*diff(y(x),x)+1; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 23

ode=x^2*D[y[x],{x,2}]==x*D[y[x],x]+1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.277 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) - x*Derivative(y(x), x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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