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]
\[ \boxed {\left (x^{2}-1\right ) y^{\prime }-2 y x -x \left (x^{2}-1\right )=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 4] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 29
dsolve([(x^2-1)*diff(y(x),x)-2*x*y(x)= x*(x^2-1),y(0) = 4],y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\left (i \pi -\ln \left (x +1\right )-\ln \left (x -1\right )+8\right ) \left (x^{2}-1\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.033 (sec). Leaf size: 27
DSolve[{(x^2-1)*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*}