14.3.15 problem Problem 15

Internal problem ID [3624]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.6, First-Order Linear Differential Equations. page 59
Problem number : Problem 15
Date solved : Tuesday, September 30, 2025 at 06:48:39 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 33

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

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

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 29

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

\begin{align*} y(x)&\to \frac {x ((m+1) \log (x)-1)}{(m+1)^2}+c_1 x^{-m} \end{align*}

✓ Sympy. Time used: 0.202 (sec). Leaf size: 29

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

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