66.1.10 problem 13

Internal problem ID [15897]
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. Exercises section 1.2. page 33
Problem number : 13
Date solved : Thursday, October 02, 2025 at 10:29:25 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 29

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

\begin{align*} y &= \sqrt {\ln \left (t^{2}+1\right )+c_1} \\ y &= -\sqrt {\ln \left (t^{2}+1\right )+c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.066 (sec). Leaf size: 41

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

\begin{align*} y(t)&\to -\sqrt {\log \left (t^2+1\right )+2 c_1}\\ y(t)&\to \sqrt {\log \left (t^2+1\right )+2 c_1} \end{align*}

✓ Sympy. Time used: 0.261 (sec). Leaf size: 29

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

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