Internal problem ID [12403]
Book: Differential Equations, Linear, Nonlinear, Ordinary, Partial. A.C. King, J.Billingham,
S.R.Otto. Cambridge Univ. Press 2003
Section: Chapter 1 VARIABLE COEFFICIENT, SECOND ORDER DIFFERENTIAL
EQUATIONS. Problems page 28
Problem number: Problem 1.8(a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x^{2}-1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }-y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 54
Order:=6; dsolve((x^2-1)^2*diff(y(x),x$2)+(x+1)*diff(y(x),x)-y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (1+\frac {1}{2} x^{2}-\frac {1}{6} x^{3}+\frac {1}{6} x^{4}-\frac {7}{60} x^{5}\right ) y \left (0\right )+\left (x -\frac {1}{2} x^{2}+\frac {1}{6} x^{3}-\frac {1}{6} x^{4}+\frac {7}{60} x^{5}\right ) D\left (y \right )\left (0\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 70
AsymptoticDSolveValue[(x^2-1)^2*y''[x]+(x+1)*y'[x]-y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (-\frac {7 x^5}{60}+\frac {x^4}{6}-\frac {x^3}{6}+\frac {x^2}{2}+1\right )+c_2 \left (\frac {7 x^5}{60}-\frac {x^4}{6}+\frac {x^3}{6}-\frac {x^2}{2}+x\right ) \]