Internal problem ID [1193]
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: 14.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x^{2}+1\right ) y^{\prime \prime }+\left (2-x \right ) y^{\prime }+3 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 52
Order:=6; dsolve((1+x^2)*diff(y(x),x$2)+(2-x)*diff(y(x),x)+3*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1-\frac {3}{2} x^{2}+x^{3}-\frac {1}{8} x^{4}-\frac {1}{4} x^{5}\right ) y \relax (0)+\left (x -x^{2}+\frac {1}{3} x^{3}+\frac {1}{12} x^{4}-\frac {2}{15} x^{5}\right ) D\relax (y )\relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 64
AsymptoticDSolveValue[(1+x^2)*y''[x]+(2-x)*y'[x]+3*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (-\frac {x^5}{4}-\frac {x^4}{8}+x^3-\frac {3 x^2}{2}+1\right )+c_2 \left (-\frac {2 x^5}{15}+\frac {x^4}{12}+\frac {x^3}{3}-x^2+x\right ) \]