Internal problem ID [1214]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 7 Series Solutions of Linear Second Equations. 7.2 SERIES SOLUTIONS NEAR
AN ORDINARY POINT I. Exercises 7.2. Page 329
Problem number: 10.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime } x +3 y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 34
Order:=6; dsolve(diff(y(x),x$2)+2*x*diff(y(x),x)+3*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (1-\frac {3}{2} x^{2}+\frac {7}{8} x^{4}\right ) y \left (0\right )+\left (x -\frac {5}{6} x^{3}+\frac {3}{8} x^{5}\right ) D\left (y \right )\left (0\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 42
AsymptoticDSolveValue[y''[x]+2*x*y'[x]+3*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (\frac {3 x^5}{8}-\frac {5 x^3}{6}+x\right )+c_1 \left (\frac {7 x^4}{8}-\frac {3 x^2}{2}+1\right ) \]