74.7.58 problem 65

Internal problem ID [16064]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.5, page 64
Problem number : 65
Date solved : Monday, March 31, 2025 at 02:38:12 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

With initial conditions

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

✓ Maple. Time used: 0.095 (sec). Leaf size: 34

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

\begin{align*} y &= \sqrt {-2 \ln \left (t \right )+4 \ln \left (2\right )}\, t \\ y &= -\sqrt {-2 \ln \left (t \right )+4 \ln \left (2\right )}\, t \\ \end{align*}

✓ Mathematica. Time used: 0.179 (sec). Leaf size: 36

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

\begin{align*} y(t)\to -t \sqrt {\log (16)-2 \log (t)} \\ y(t)\to t \sqrt {\log (16)-2 \log (t)} \\ \end{align*}

✓ Sympy. Time used: 0.426 (sec). Leaf size: 32

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

\[ \left [ y{\left (t \right )} = - t \sqrt {- 2 \log {\left (t \right )} + \log {\left (16 \right )}}, \ y{\left (t \right )} = t \sqrt {- 2 \log {\left (t \right )} + \log {\left (16 \right )}}\right ] \]