Internal problem ID [5305]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 4. Linear equations with Regular Singular Points. Page 166
Problem number: 3(c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+5 x y^{\prime }+\left (-x^{3}+3\right ) y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 35
Order:=8; dsolve(x^2*diff(y(x),x$2)+5*x*diff(y(x),x)+(3-x^3)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \frac {c_{1} \left (1+\frac {1}{15} x^{3}+\frac {1}{720} x^{6}+\mathrm {O}\left (x^{8}\right )\right )}{x}+\frac {c_{2} \left (-2-\frac {2}{3} x^{3}-\frac {1}{36} x^{6}+\mathrm {O}\left (x^{8}\right )\right )}{x^{3}} \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 40
AsymptoticDSolveValue[x^2*y''[x]+5*x*y'[x]+(3-3*x^3)*y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_1 \left (\frac {x^3}{8}+\frac {1}{x^3}+1\right )+c_2 \left (\frac {x^5}{80}+\frac {x^2}{5}+\frac {1}{x}\right ) \]