68.4.45 problem 45

Internal problem ID [17225]
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 : 45
Date solved : Thursday, October 02, 2025 at 01:58:50 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=2 \\ \end{align*}

✓ Maple. Time used: 0.085 (sec). Leaf size: 15

ode:=diff(y(t),t) = t^(1/2)/y(t); 
ic:=[y(0) = 2]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = \frac {2 \sqrt {9+3 t^{{3}/{2}}}}{3} \]

✓ Mathematica. Time used: 1.678 (sec). Leaf size: 23

ode=D[y[t],t]==Sqrt[t]/y[t]; 
ic={y[0]==2}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {2 \sqrt {t^{3/2}+3}}{\sqrt {3}} \end{align*}

✓ Sympy. Time used: 0.189 (sec). Leaf size: 15

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

\[ y{\left (t \right )} = \frac {\sqrt {12 t^{\frac {3}{2}} + 36}}{3} \]