73.17.38 problem 38

Internal problem ID [15501]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 25. Review exercises for part III. page 447
Problem number : 38
Date solved : Monday, March 31, 2025 at 01:39:40 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y&=18 \ln \left (x \right ) \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 20

ode:=x^2*diff(diff(y(x),x),x)+2*x*diff(y(x),x)-6*y(x) = 18*ln(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_2}{x^{3}}+c_1 \,x^{2}-3 \ln \left (x \right )-\frac {1}{2} \]

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 25

ode=x^2*D[y[x],{x,2}]+2*x*D[y[x],x]-6*y[x]==18*Log[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {c_1}{x^3}+c_2 x^2-3 \log (x)-\frac {1}{2} \]

✓ Sympy. Time used: 0.264 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + 2*x*Derivative(y(x), x) - 6*y(x) - 18*log(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1}}{x^{3}} + C_{2} x^{2} - 3 \log {\left (x \right )} - \frac {1}{2} \]