Internal problem ID [1190]
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: 11.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (2+x \right ) y^{\prime \prime }+y^{\prime } x +3 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 49
Order:=6; dsolve((2+x)*diff(y(x),x$2)+x*diff(y(x),x)+3*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1-\frac {3}{4} x^{2}+\frac {1}{8} x^{3}+\frac {1}{8} x^{4}-\frac {9}{160} x^{5}\right ) y \relax (0)+\left (x -\frac {1}{3} x^{3}+\frac {1}{12} x^{4}+\frac {1}{40} x^{5}\right ) D\relax (y )\relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 63
AsymptoticDSolveValue[(2+x)*y''[x]+x*y'[x]+3*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (\frac {x^5}{40}+\frac {x^4}{12}-\frac {x^3}{3}+x\right )+c_1 \left (-\frac {9 x^5}{160}+\frac {x^4}{8}+\frac {x^3}{8}-\frac {3 x^2}{4}+1\right ) \]