12.2.36 problem 36

Internal problem ID [1572]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Linear first order. Section 2.1 Page 41
Problem number : 36
Date solved : Saturday, March 29, 2025 at 10:59:49 PM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (0\right )&=4 \end{align*}

✓ Maple. Time used: 0.042 (sec). Leaf size: 28

ode:=(x^2-1)*diff(y(x),x)-2*x*y(x) = x*(x^2-1); 
ic:=y(0) = 4; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = -\frac {\left (i \pi -\ln \left (x -1\right )-\ln \left (x +1\right )+8\right ) \left (x^{2}-1\right )}{2} \]

✓ Mathematica. Time used: 0.033 (sec). Leaf size: 27

ode=(x^2-1)*D[y[x],x]-2*x*y[x]== x*(x^2-1); 
ic=y[0]==4; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{2} \left (x^2-1\right ) \left (\log \left (x^2-1\right )-i \pi -8\right ) \]

✓ Sympy. Time used: 0.349 (sec). Leaf size: 41

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

\[ y{\left (x \right )} = \frac {x^{2} \log {\left (x^{2} - 1 \right )}}{2} + x^{2} \left (-4 - \frac {i \pi }{2}\right ) - \frac {\log {\left (x^{2} - 1 \right )}}{2} + 4 + \frac {i \pi }{2} \]