Internal problem ID [5815]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 2. Linear homogeneous equations. Section 2.2 problems. page 95
Problem number: 54.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-x^{2}+1\right ) y^{\prime }-2 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 47
dsolve(x^2*(1-x^2)*diff(y(x),x$2)+2*x*(1-x^2)*diff(y(x),x)-2*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{2} \left (x^{2}-1\right ) \ln \left (x -1\right )+\left (-x^{2}+1\right ) c_{2} \ln \left (x +1\right )+2 c_{1} x^{2}-2 c_{2} x -2 c_{1}}{2 x^{2}} \]
✓ Solution by Mathematica
Time used: 0.06 (sec). Leaf size: 56
DSolve[x^2*(1-x^2)*y''[x]+2*x*(1-x^2)*y'[x]-2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {-4 c_1 x^2-c_2 \left (x^2-1\right ) \log (1-x)+c_2 \left (x^2-1\right ) \log (x+1)+2 c_2 x+4 c_1}{4 x^2} \]