Internal problem ID [6332]
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]]
\[ \boxed {\left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y=\left (x^{2}-1\right )^{2}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 20
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)
\[ y \left (x \right ) = c_{2} x +c_{1} x^{2}+c_{1} +\frac {1}{2}+\frac {1}{6} x^{4} \]
✓ Solution by Mathematica
Time used: 0.375 (sec). Leaf size: 111
DSolve[(x^2-1)*y''[x]-2*x*y'[x]+2*y[x]==(x^2-1)^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {-x^6+4 x^4-2 x^3+3 x^2 \left (-1+2 c_1 \sqrt {-\left (x^2-1\right )^2}\right )+2 x \left (-6 c_1 \sqrt {-\left (x^2-1\right )^2}+3 c_2 \sqrt {-\left (x^2-1\right )^2}+1\right )+6 c_1 \sqrt {-\left (x^2-1\right )^2}}{6-6 x^2} \]