74.4.46 problem 46

Internal problem ID [15868]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number : 46
Date solved : Monday, March 31, 2025 at 02:10:52 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

With initial conditions

\begin{align*} y \left (1\right )&=2 \end{align*}

✓ Maple. Time used: 0.344 (sec). Leaf size: 94

ode:=diff(y(t),t) = (y(t)/t)^(1/2); 
ic:=y(1) = 2; 
dsolve([ode,ic],y(t), singsol=all);
 

\begin{align*} y &= \frac {{\left (\left (t^{2}\right )^{{1}/{4}} \left (\sqrt {2}-1\right )+t \right )}^{2}}{t} \\ y &= \frac {{\left (\left (t^{2}\right )^{{1}/{4}} \sqrt {2}+\left (t^{2}\right )^{{1}/{4}}-t \right )}^{2}}{t} \\ y &= \left (-2+2 \sqrt {2}\right ) \sqrt {t}+t -2 \sqrt {2}+3 \\ y &= \left (-2 \sqrt {2}-2\right ) \sqrt {t}+t +2 \sqrt {2}+3 \\ \end{align*}

✓ Mathematica. Time used: 0.17 (sec). Leaf size: 57

ode=D[y[t],t]==Sqrt[y[t]/t]; 
ic={y[1]==2}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)\to t-2 \left (1+\sqrt {2}\right ) \sqrt {t}+2 \sqrt {2}+3 \\ y(t)\to t+2 \left (\sqrt {2}-1\right ) \sqrt {t}-2 \sqrt {2}+3 \\ \end{align*}

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-sqrt(y(t)/t) + Derivative(y(t), t),0) 
ics = {y(1): 2} 
dsolve(ode,func=y(t),ics=ics)
 

NotImplementedError : Initial conditions produced too many solutions for constants