14.3.5 problem Problem 5

Internal problem ID [3614]
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 5
Date solved : Tuesday, September 30, 2025 at 06:48:32 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }+\frac {2 x y}{-x^{2}+1}&=4 x \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 24

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

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

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 22

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

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

✓ Sympy. Time used: 0.226 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*x + 2*x*y(x)/(1 - x**2) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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