46.2.16 problem 18

Internal problem ID [7319]
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
Date solved : Monday, January 27, 2025 at 02:50:17 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 \left (t^{2}-3 t +2\right ) y^{\prime \prime }-2 y^{\prime }+y&=0 \end{align*}

Using series method with expansion around

\begin{align*} 0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 59

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);
 

\[ y = \left (1-\frac {1}{16} t^{2}-\frac {7}{192} t^{3}-\frac {73}{3072} t^{4}-\frac {1037}{61440} t^{5}\right ) y \left (0\right )+\left (t +\frac {1}{8} t^{2}+\frac {5}{96} t^{3}+\frac {47}{1536} t^{4}+\frac {643}{30720} t^{5}\right ) y^{\prime }\left (0\right )+O\left (t^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 70

AsymptoticDSolveValue[4*(t^2-3*t+2)*D[y[t],{t,2}]-2*D[y[t],t]+y[t]==0,y[t],{t,0,"6"-1}]
 

\[ y(t)\to c_1 \left (-\frac {1037 t^5}{61440}-\frac {73 t^4}{3072}-\frac {7 t^3}{192}-\frac {t^2}{16}+1\right )+c_2 \left (\frac {643 t^5}{30720}+\frac {47 t^4}{1536}+\frac {5 t^3}{96}+\frac {t^2}{8}+t\right ) \]