90.20.4 problem 4

Internal problem ID [25299]
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 : 4
Date solved : Thursday, October 02, 2025 at 11:59:41 PM
CAS classification : [NONE]

\begin{align*} y^{\prime \prime }+t y^{\prime }+\left (t^{2}+1\right )^{2} y^{2}&=0 \end{align*}

✗ Maple

ode:=diff(diff(y(t),t),t)+t*diff(y(t),t)+(t^2+1)^2*y(t)^2 = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[t],{t,2}]+t*D[y[t],{t,1}]+(1+t^2)*y[t]^2==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

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

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