72.2.22 problem 16 (vii)

Internal problem ID [14578]
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 1.3 page 47
Problem number : 16 (vii)
Date solved : Thursday, March 13, 2025 at 03:36:30 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 14

ode:=diff(y(t),t) = t+t*y(t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = -1+c_{1} {\mathrm e}^{\frac {t^{2}}{2}} \]

✓ Mathematica. Time used: 0.052 (sec). Leaf size: 24

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

\begin{align*} y(t)\to -1+c_1 e^{\frac {t^2}{2}} \\ y(t)\to -1 \\ \end{align*}

✓ Sympy. Time used: 0.276 (sec). Leaf size: 12

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

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