81.7.2 problem 3

Internal problem ID [18628]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter VI. Certain particular forms of equations. Exercises at page 74
Problem number : 3
Date solved : Monday, March 31, 2025 at 05:47:01 PM
CAS classification : [[_2nd_order, _quadrature]]

\begin{align*} x^{2} y^{\prime \prime }&=\ln \left (x \right ) \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 19

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

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

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 24

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

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

✓ Sympy. Time used: 0.160 (sec). Leaf size: 17

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

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