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 : Monday, January 27, 2025 at 05:00:45 AM
CAS classification : [_linear]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 24

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

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

✓ Solution by Mathematica

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

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

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