Internal problem ID [4898]
Book: ADVANCED ENGINEERING MATHEMATICS. ERWIN KREYSZIG, HERBERT KREYSZIG,
EDWARD J. NORMINTON. 10th edition. John Wiley USA. 2011
Section: Chapter 5. Series Solutions of ODEs. Special Functions. Problem set 5.3. Extended Power
Series Method: Frobenius Method page 186
Problem number: 18.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {4 \left (t^{2}-3 t +2\right ) y^{\prime \prime }-2 y^{\prime }+y=0} \end {gather*} With the expansion point for the power series method at \(t = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 54
Order:=6; dsolve(4*(t^2-3*t+2)*diff(y(t),t$2)-2*diff(y(t),t)+y(t)=0,y(t),type='series',t=0);
\[ y \relax (t ) = \left (1-\frac {1}{16} t^{2}-\frac {7}{192} t^{3}-\frac {73}{3072} t^{4}-\frac {1037}{61440} t^{5}\right ) y \relax (0)+\left (t +\frac {1}{8} t^{2}+\frac {5}{96} t^{3}+\frac {47}{1536} t^{4}+\frac {643}{30720} t^{5}\right ) D\relax (y )\relax (0)+O\left (t^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 70
AsymptoticDSolveValue[4*(t^2-3*t+2)*y''[t]-2*y'[t]+y[t]==0,y[t],{t,0,5}]
\[ y(t)\to c_1 \left (-\frac {1037 t^5}{61440}-\frac {73 t^4}{3072}-\frac {7 t^3}{192}-\frac {t^2}{16}+1\right )+c_2 \left (\frac {643 t^5}{30720}+\frac {47 t^4}{1536}+\frac {5 t^3}{96}+\frac {t^2}{8}+t\right ) \]