Internal problem ID [2408]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 42, page 206
Problem number: 7.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }+x \left (x^{2}-1\right ) y^{\prime }+\left (-x^{2}+1\right ) y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 37
Order:=6; dsolve(x^2*diff(y(x),x$2)+x*(x^2-1)*diff(y(x),x)+(1-x^2)*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (\left (c_{2} \ln \left (x \right )+c_{1} \right ) \left (1+\operatorname {O}\left (x^{6}\right )\right )+\left (-\frac {1}{4} x^{2}+\frac {1}{32} x^{4}+\operatorname {O}\left (x^{6}\right )\right ) c_{2} \right ) x \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 33
AsymptoticDSolveValue[x^2*y''[x]+x*(x^2-1)*y'[x]+(1-x^2)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (x \left (\frac {x^4}{32}-\frac {x^2}{4}\right )+x \log (x)\right )+c_1 x \]