72.8.11 problem 24

Internal problem ID [14704]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Review Exercises for chapter 1. page 136
Problem number : 24
Date solved : Monday, March 31, 2025 at 12:54:31 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 13

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

\[ y = c_1 \sqrt {t^{2}+1} \]

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 22

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

\begin{align*} y(t)\to c_1 \sqrt {t^2+1} \\ y(t)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.205 (sec). Leaf size: 12

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

\[ y{\left (t \right )} = C_{1} \sqrt {t^{2} + 1} \]