Internal problem ID [2412]
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: 11.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-9 y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 43
Order:=6; dsolve(x^2*(1-x)*diff(y(x),x$2)+x*(1+x)*diff(y(x),x)-9*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = c_{1} x^{3} \left (1+\frac {3}{7} x +\frac {3}{14} x^{2}+\frac {5}{42} x^{3}+\frac {1}{14} x^{4}+\frac {1}{22} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+\frac {c_{2} \left (-86400+259200 x -259200 x^{2}+86400 x^{3}+\operatorname {O}\left (x^{6}\right )\right )}{x^{3}} \]
✓ Solution by Mathematica
Time used: 0.032 (sec). Leaf size: 57
AsymptoticDSolveValue[x^2*(1-x)*y''[x]+x*(1+x)*y'[x]-9*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {1}{x^3}-\frac {3}{x^2}+\frac {3}{x}-1\right )+c_2 \left (\frac {x^7}{14}+\frac {5 x^6}{42}+\frac {3 x^5}{14}+\frac {3 x^4}{7}+x^3\right ) \]