Internal problem ID [5579]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 2. Second-Order Linear Equations. Section 2.3. THE METHOD OF VARIATION OF
PARAMETERS. Page 71
Problem number: 5(a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y-\left (x^{2}-1\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve((x^2-1)*diff(y(x),x$2)-2*x*diff(y(x),x)+2*y(x)=(x^2-1)^2,y(x), singsol=all)
\[ y \relax (x ) = c_{2} x +\left (x^{2}+1\right ) c_{1}+\frac {1}{2}+\frac {x^{4}}{6} \]
✓ Solution by Mathematica
Time used: 3.48 (sec). Leaf size: 96
DSolve[(x^2-1)*y''[x]-2*x*y'[x]+2*y[x]==(x^2-1)^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x \left (x^5-4 x^3+2 x^2-6 c_1 \sqrt {-\left (x^2-1\right )^2} x+6 (2 c_1-c_2) \sqrt {-\left (x^2-1\right )^2}+3 x-2\right )-6 c_1 \sqrt {-\left (x^2-1\right )^2}}{6 \left (x^2-1\right )} \\ \end{align*}