87.18.17 problem 17

Internal problem ID [23658]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 135
Problem number : 17
Date solved : Thursday, October 02, 2025 at 09:43:56 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y&=\ln \left (x \right ) \left (\frac {1}{x^{3}}+\frac {1}{x^{5}}\right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 38

ode:=x^2*diff(diff(y(x),x),x)+5*x*diff(y(x),x)+4*y(x) = ln(x)*(1/x^3+1/x^5); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (27 c_1 \,x^{3}+27 x^{2}+3\right ) \ln \left (x \right )+27 c_2 \,x^{3}+54 x^{2}+2}{27 x^{5}} \]

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 44

ode=x^2*D[y[x],{x,2}]+5*x*D[y[x],x]+4*y[x]==Log[x]*(1/x^3+1/x^5); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {27 c_1 x^3+54 x^2+3 \left (18 c_2 x^3+9 x^2+1\right ) \log (x)+2}{27 x^5} \end{align*}

✓ Sympy. Time used: 0.290 (sec). Leaf size: 36

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + 5*x*Derivative(y(x), x) - (x**(-3) + x**(-5))*log(x) + 4*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {27 x^{3} \left (C_{1} + C_{2} \log {\left (x \right )}\right ) + 27 x^{2} \left (\log {\left (x \right )} + 2\right ) + 3 \log {\left (x \right )} + 2}{27 x^{5}} \]