Internal problem ID [2407]
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: 6.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }-5 x y^{\prime }+9 y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 51
Order:=6; dsolve(x^2*(1-x^2)*diff(y(x),x$2)-5*x*diff(y(x),x)+9*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (\left (c_{2} \ln \left (x \right )+c_{1} \right ) \left (1+\frac {3}{2} x^{2}+\frac {15}{8} x^{4}+\operatorname {O}\left (x^{6}\right )\right )+\left (-\frac {1}{4} x^{2}-\frac {13}{32} x^{4}+\operatorname {O}\left (x^{6}\right )\right ) c_{2} \right ) x^{3} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 71
AsymptoticDSolveValue[x^2*(1-x^2)*y''[x]-5*x*y'[x]+9*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {15 x^4}{8}+\frac {3 x^2}{2}+1\right ) x^3+c_2 \left (\left (-\frac {13 x^4}{32}-\frac {x^2}{4}\right ) x^3+\left (\frac {15 x^4}{8}+\frac {3 x^2}{2}+1\right ) x^3 \log (x)\right ) \]