87.2.7 problem 7

Internal problem ID [23242]
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 1. Elementary methods. First order differential equations. Exercise at page 17
Problem number : 7
Date solved : Thursday, October 02, 2025 at 09:25:11 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 34

ode:=x*diff(y(x),x)+y(x)/(2*x+3) = ln(x-2); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 1.168 (sec). Leaf size: 52

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

\begin{align*} y(x)&\to \frac {\sqrt [3]{2 x+3} \left (\int _1^x\frac {\log (K[1]-2)}{K[1]^{2/3} \sqrt [3]{2 K[1]+3}}dK[1]+c_1\right )}{\sqrt [3]{x}} \end{align*}

✓ Sympy. Time used: 40.364 (sec). Leaf size: 570

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

\[ \text {Solution too large to show} \]