Internal problem ID [922]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {\left (x^{2}-1\right ) y^{\prime }-2 y x -\left (x^{2}-1\right ) x=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 4] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 25
dsolve([(x^2-1)*diff(y(x),x)-2*x*y(x)= x*(x^2-1),y(0) = 4],y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (-i \pi +\ln \left (x +1\right )+\ln \left (x -1\right )-8\right ) \left (x^{2}-1\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.036 (sec). Leaf size: 27
DSolve[{(x^2-1)*y'[x]-2*x*y[x]== x*(x^2-1),y[0]==4},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (x^2-1\right ) \left (\log \left (x^2-1\right )-i \pi -8\right ) \\ \end{align*}