90.25.15 problem 15

Internal problem ID [25396]
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 379
Problem number : 15
Date solved : Friday, October 03, 2025 at 12:01:05 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} t y^{\prime \prime }-y^{\prime }+4 t^{3} y&=4 t^{5} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 20

ode:=t*diff(diff(y(t),t),t)-diff(y(t),t)+4*t^3*y(t) = 4*t^5; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \sin \left (t^{2}\right ) c_2 +\cos \left (t^{2}\right ) c_1 +t^{2} \]

✓ Mathematica. Time used: 0.029 (sec). Leaf size: 23

ode=t*D[y[t],{t,2}]-D[y[t],t]+4*t^3*y[t]==4*t^5; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to t^2+c_1 \cos \left (t^2\right )+c_2 \sin \left (t^2\right ) \end{align*}

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-4*t**5 + 4*t**3*y(t) + t*Derivative(y(t), (t, 2)) - Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

NotImplementedError : The given ODE -t*(-4*t**4 + 4*t**2*y(t) + Derivative(y(t), (t, 2))) + Derivati