83.26.8 problem 8

Internal problem ID [19253]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VI. Homogeneous linear equations with variable coefficients. Exercise VI (C) at page 93
Problem number : 8
Date solved : Thursday, March 13, 2025 at 02:04:55 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 22

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

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

✓ Mathematica. Time used: 0.032 (sec). Leaf size: 27

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

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

✓ Sympy. Time used: 0.226 (sec). Leaf size: 17

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

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