73.1.7 problem 2.2 (g)

Internal problem ID [14914]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 2. Integration and differential equations. Additional exercises. page 32
Problem number : 2.2 (g)
Date solved : Monday, March 31, 2025 at 01:03:51 PM
CAS classification : [[_2nd_order, _quadrature]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 13

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

\[ y = -\ln \left (x \right )+c_1 x +c_2 \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 16

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

\[ y(x)\to -\log (x)+c_2 x+c_1 \]

✓ Sympy. Time used: 0.214 (sec). Leaf size: 10

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

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