72.1.27 problem 30

Internal problem ID [14548]
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 : 30
Date solved : Thursday, March 13, 2025 at 03:33:29 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=4 \end{align*}

✓ Maple. Time used: 0.729 (sec). Leaf size: 23

ode:=diff(y(t),t) = t/(y(t)-t^2*y(t)); 
ic:=y(0) = 4; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = \sqrt {i \pi -\ln \left (t -1\right )-\ln \left (t +1\right )+16} \]

✓ Mathematica. Time used: 0.089 (sec). Leaf size: 24

ode=D[y[t],t]==t/(y[t]-t^2*y[t]); 
ic={y[0]==4}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \sqrt {-\log \left (t^2-1\right )+i \pi +16} \]

✓ Sympy. Time used: 0.580 (sec). Leaf size: 17

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

\[ y{\left (t \right )} = \sqrt {- \log {\left (t^{2} - 1 \right )} + 16 + i \pi } \]