87.18.4 problem 4

Internal problem ID [23645]
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 : 4
Date solved : Thursday, October 02, 2025 at 09:43:46 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+10 y^{\prime }+25 y&=\frac {{\mathrm e}^{-5 x} \ln \left (x \right )}{x^{2}} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 25

ode:=diff(diff(y(x),x),x)+10*diff(y(x),x)+25*y(x) = exp(-5*x)*ln(x)/x^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-5 x} \left (c_2 +c_1 x -\frac {\ln \left (x \right )^{2}}{2}-\ln \left (x \right )-1\right ) \]

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 35

ode=D[y[x],{x,2}]+10*D[y[x],x]+25*y[x]==Exp[-5*x]*Log[x]/x^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{2} e^{-5 x} \left (-\log ^2(x)-2 \log (x)+2 (c_2 x-1+c_1)\right ) \end{align*}

✓ Sympy. Time used: 0.233 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(25*y(x) + 10*Derivative(y(x), x) + Derivative(y(x), (x, 2)) - exp(-5*x)*log(x)/x**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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