90.30.4 problem 4

Internal problem ID [25444]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 7. Power series methods. Exercises at page 517
Problem number : 4
Date solved : Friday, October 03, 2025 at 12:01:35 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 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:=diff(diff(y(t),t),t)-3*diff(y(t),t)+2*y(t) = 0; 
dsolve(ode,y(t),type='series',t=0);
 

\[ y = \left (1-t^{2}-t^{3}-\frac {7}{12} t^{4}-\frac {1}{4} t^{5}\right ) y \left (0\right )+\left (t +\frac {3}{2} t^{2}+\frac {7}{6} t^{3}+\frac {5}{8} t^{4}+\frac {31}{120} t^{5}\right ) y^{\prime }\left (0\right )+O\left (t^{6}\right ) \]

✓ Mathematica. Time used: 0.0 (sec). Leaf size: 66

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

\[ y(t)\to c_1 \left (-\frac {t^5}{4}-\frac {7 t^4}{12}-t^3-t^2+1\right )+c_2 \left (\frac {31 t^5}{120}+\frac {5 t^4}{8}+\frac {7 t^3}{6}+\frac {3 t^2}{2}+t\right ) \]

✓ Sympy. Time used: 0.239 (sec). Leaf size: 46

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

\[ y{\left (t \right )} = C_{2} \left (- \frac {7 t^{4}}{12} - t^{3} - t^{2} + 1\right ) + C_{1} t \left (\frac {5 t^{3}}{8} + \frac {7 t^{2}}{6} + \frac {3 t}{2} + 1\right ) + O\left (t^{6}\right ) \]