14.1.7 problem 7

Internal problem ID [2478]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 1. First order differential equations. Section 1.2. Linear equations. Excercises page 9
Problem number : 7
Date solved : Sunday, March 30, 2025 at 12:02:40 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }+\frac {t y}{t^{2}+1}&=1-\frac {t^{3} y}{t^{4}+1} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 38

ode:=diff(y(t),t)+t/(t^2+1)*y(t) = 1-t^3/(t^4+1)*y(t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {\int \sqrt {t^{2}+1}\, \left (t^{4}+1\right )^{{1}/{4}}d t +c_1}{\sqrt {t^{2}+1}\, \left (t^{4}+1\right )^{{1}/{4}}} \]

✓ Mathematica. Time used: 0.989 (sec). Leaf size: 55

ode=D[y[t],t]+t/(1+t^2)*y[t]==1-t^3/(1+t^4)*y[t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \frac {\int _1^t\sqrt {K[1]^2+1} \sqrt [4]{K[1]^4+1}dK[1]+c_1}{\sqrt {t^2+1} \sqrt [4]{t^4+1}} \]

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(t**3*y(t)/(t**4 + 1) + t*y(t)/(t**2 + 1) + Derivative(y(t), t) - 1,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

Timed Out