74.7.28 problem 28

Internal problem ID [16026]
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 : 28
Date solved : Thursday, March 13, 2025 at 07:19:34 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} y-\left (3 \sqrt {t y}+t \right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.010 (sec). Leaf size: 21

ode:=y(t)-(3*(t*y(t))^(1/2)+t)*diff(y(t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ 3 \ln \left (y\right )-\frac {2 t}{\sqrt {t y}}-c_{1} = 0 \]

✓ Mathematica. Time used: 0.223 (sec). Leaf size: 33

ode=y[t]-(3*Sqrt[t*y[t]]+t)*D[y[t],t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [3 \log \left (\frac {y(t)}{t}\right )-\frac {2}{\sqrt {\frac {y(t)}{t}}}=-3 \log (t)+c_1,y(t)\right ] \]

✓ Sympy. Time used: 3.536 (sec). Leaf size: 42

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-(t + 3*sqrt(t*y(t)))*Derivative(y(t), t) + y(t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ \left [ y{\left (t \right )} = e^{C_{1} + 2 W\left (- \frac {\sqrt {t} e^{- \frac {C_{1}}{2}}}{3}\right )}, \ y{\left (t \right )} = e^{C_{1} + 2 W\left (\frac {\sqrt {t} e^{- \frac {C_{1}}{2}}}{3}\right )}\right ] \]