46.2.17 problem 19

Internal problem ID [7320]
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 : 19
Date solved : Wednesday, March 05, 2025 at 04:23:17 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 \left (t^{2}-5 t +6\right ) y^{\prime \prime }+\left (2 t -3\right ) y^{\prime }-8 y&=0 \end{align*}

Using series method with expansion around

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

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

Order:=6; 
ode:=2*(t^2-5*t+6)*diff(diff(y(t),t),t)+(2*t-3)*diff(y(t),t)-8*y(t) = 0; 
dsolve(ode,y(t),type='series',t=0);
 

\[ y = \left (1+\frac {1}{3} t^{2}+\frac {13}{108} t^{3}+\frac {299}{5184} t^{4}+\frac {923}{34560} t^{5}\right ) y \left (0\right )+\left (t +\frac {1}{8} t^{2}+\frac {37}{288} t^{3}+\frac {851}{13824} t^{4}+\frac {2627}{92160} t^{5}\right ) y^{\prime }\left (0\right )+O\left (t^{6}\right ) \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 70

ode=2*(t^2-5*t+6)*D[y[t],{t,2}]+(2*t-3)*D[y[t],t]-8*y[t]==0; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[t],{t,0,5}]
 

\[ y(t)\to c_1 \left (\frac {923 t^5}{34560}+\frac {299 t^4}{5184}+\frac {13 t^3}{108}+\frac {t^2}{3}+1\right )+c_2 \left (\frac {2627 t^5}{92160}+\frac {851 t^4}{13824}+\frac {37 t^3}{288}+\frac {t^2}{8}+t\right ) \]

✓ Sympy. Time used: 1.078 (sec). Leaf size: 49

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq((2*t - 3)*Derivative(y(t), t) + (2*t**2 - 10*t + 12)*Derivative(y(t), (t, 2)) - 8*y(t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics,hint="2nd_power_series_ordinary",x0=0,n=6)
 

\[ y{\left (t \right )} = C_{2} \left (\frac {299 t^{4}}{5184} + \frac {13 t^{3}}{108} + \frac {t^{2}}{3} + 1\right ) + C_{1} t \left (\frac {851 t^{3}}{13824} + \frac {37 t^{2}}{288} + \frac {t}{8} + 1\right ) + O\left (t^{6}\right ) \]