80.1.3 problem 4

Internal problem ID [21121]
Book : A Textbook on Ordinary Differential Equations by Shair Ahmad and Antonio Ambrosetti. Second edition. ISBN 978-3-319-16407-6. Springer 2015
Section : Chapter 1. First order linear differential equations. Excercise 1.5 at page 13
Problem number : 4
Date solved : Thursday, October 02, 2025 at 07:08:39 PM
CAS classification : [_separable]

\begin{align*} x^{\prime }+\frac {\left (2 t^{3}+\sin \left (t \right )+5\right ) x}{t^{12}+5}&=0 \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 5

ode:=diff(x(t),t)+(2*t^3+sin(t)+5)/(t^12+5)*x(t) = 0; 
ic:=[x(0) = 0]; 
dsolve([ode,op(ic)],x(t), singsol=all);
 

\[ x = 0 \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 6

ode=D[x[t],t]+(2*t^3+Sin[t]+5)/(t^(12)+5)*x[t]==0; 
ic={x[0]==0}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to 0 \end{align*}

✗ Sympy

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(Derivative(x(t), t) + (2*t**3 + sin(t) + 5)*x(t)/(t**12 + 5),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

Timed Out