36.3.9 problem 9

Internal problem ID [6330]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.4, Exact equations. Exercises. page 64
Problem number : 9
Date solved : Wednesday, March 05, 2025 at 12:35:13 AM
CAS classification : [_linear]

\begin{align*} 2 x y+3+\left (x^{2}-1\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

ode:=2*x*y(x)+3+(x^2-1)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = \frac {-3 x +c_{1}}{x^{2}-1} \]

✓ Mathematica. Time used: 0.032 (sec). Leaf size: 19

ode=(2*x*y[x]+3)+(x^2-1)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {-3 x+c_1}{x^2-1} \]

✓ Sympy. Time used: 0.238 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x*y(x) + (x**2 - 1)*Derivative(y(x), x) + 3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} - 3 x}{x^{2} - 1} \]