90.20.28 problem 18 (3 a)

Internal problem ID [25323]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 5. Second Order Linear Differential Equations. Exercises at page 337
Problem number : 18 (3 a)
Date solved : Friday, October 03, 2025 at 12:00:04 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y&=t^{5} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=1 \\ y^{\prime }\left (1\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.008 (sec). Leaf size: 17

ode:=t^2*diff(diff(y(t),t),t)-4*t*diff(y(t),t)+6*y(t) = t^5; 
ic:=[y(1) = 1, D(y)(1) = 0]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = \frac {t^{2} \left (t^{3}-15 t +20\right )}{6} \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 20

ode=t^2*D[y[t],{t,2}]-4*t*D[y[t],t]+6*y[t]==t^5; 
ic={y[1]==1,Derivative[1][y][1] ==0}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {1}{6} t^2 \left (t^3-15 t+20\right ) \end{align*}

✓ Sympy. Time used: 0.226 (sec). Leaf size: 19

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-t**5 + t**2*Derivative(y(t), (t, 2)) - 4*t*Derivative(y(t), t) + 6*y(t),0) 
ics = {y(1): 1, Subs(Derivative(y(t), t), t, 1): 0} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = t^{2} \left (\frac {t^{3}}{6} - \frac {5 t}{2} + \frac {10}{3}\right ) \]