90.7.5 problem 5

Internal problem ID [25159]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 1. First order differential equations. Exercises at page 99
Problem number : 5
Date solved : Thursday, October 02, 2025 at 11:55:31 PM
CAS classification : [_separable]

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

With initial conditions

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

✓ Maple. Time used: 0.019 (sec). Leaf size: 13

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

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

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 16

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

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

✓ Sympy. Time used: 0.150 (sec). Leaf size: 14

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

\[ y{\left (t \right )} = \frac {e^{\frac {t^{2}}{2}}}{e^{\frac {1}{2}}} \]