Internal problem ID [1765]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.8, Series solutions. Page 195
Problem number: 1.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+t y^{\prime }+y=0} \end {gather*} With the expansion point for the power series method at \(t = 0\).
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 34
Order:=6; dsolve(diff(y(t),t$2)+t*diff(y(t),t)+y(t)=0,y(t),type='series',t=0);
\[ y \relax (t ) = \left (1-\frac {1}{2} t^{2}+\frac {1}{8} t^{4}\right ) y \relax (0)+\left (t -\frac {1}{3} t^{3}+\frac {1}{15} t^{5}\right ) D\relax (y )\relax (0)+O\left (t^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 42
AsymptoticDSolveValue[y''[t]+t*y'[t]+y[t]==0,y[t],{t,0,5}]
\[ y(t)\to c_2 \left (\frac {t^5}{15}-\frac {t^3}{3}+t\right )+c_1 \left (\frac {t^4}{8}-\frac {t^2}{2}+1\right ) \]