14.2.16 problem 17

Internal problem ID [2504]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 1. First order differential equations. Section 1.4 separable equations. Excercises page 24
Problem number : 17
Date solved : Sunday, March 30, 2025 at 12:04:48 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} \left (t -\sqrt {t y}\right ) y^{\prime }&=y \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 19

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

\[ \ln \left (y\right )+\frac {2 t}{\sqrt {t y}}-c_1 = 0 \]

✓ Mathematica. Time used: 0.234 (sec). Leaf size: 31

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

\[ \text {Solve}\left [\frac {2}{\sqrt {\frac {y(t)}{t}}}+\log \left (\frac {y(t)}{t}\right )=-\log (t)+c_1,y(t)\right ] \]

✓ Sympy. Time used: 1.812 (sec). Leaf size: 39

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

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