66.1.23 problem 26

Internal problem ID [15910]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.2. page 33
Problem number : 26
Date solved : Thursday, October 02, 2025 at 10:29:48 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=3 \\ \end{align*}

✓ Maple. Time used: 0.025 (sec). Leaf size: 12

ode:=diff(y(t),t) = t*y(t); 
ic:=[y(0) = 3]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = 3 \,{\mathrm e}^{\frac {t^{2}}{2}} \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 16

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

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

✓ Sympy. Time used: 0.159 (sec). Leaf size: 10

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

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