Internal problem ID [1194]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 7 Series Solutions of Linear Second Equations. 7.1 Exercises. Page 318
Problem number: 15.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (3 x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +4 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 32
Order:=6; dsolve((1+3*x^2)*diff(y(x),x$2)-2*x*diff(y(x),x)+4*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (x^{4}-2 x^{2}+1\right ) y \relax (0)+\left (x -\frac {1}{3} x^{3}+\frac {4}{15} x^{5}\right ) D\relax (y )\relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 36
AsymptoticDSolveValue[(1+3*x^2)*y''[x]-2*x*y'[x]+4*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (\frac {4 x^5}{15}-\frac {x^3}{3}+x\right )+c_1 \left (x^4-2 x^2+1\right ) \]