68.3.7 problem 7

Internal problem ID [17154]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.1, page 32
Problem number : 7
Date solved : Thursday, October 02, 2025 at 01:45:21 PM
CAS classification : [_separable]

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

With initial conditions

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

✓ Maple. Time used: 0.045 (sec). Leaf size: 18

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

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

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 18

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

\begin{align*} y(t)&\to e^{\frac {2}{3} \left (t^{3/2}-1\right )} \end{align*}

✓ Sympy. Time used: 0.140 (sec). Leaf size: 17

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

\[ y{\left (t \right )} = \frac {e^{\frac {2 t^{\frac {3}{2}}}{3}}}{e^{\frac {2}{3}}} \]