88.1.4 problem 18

Internal problem ID [23947]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 1. Introduction. Exercise at page 6
Problem number : 18
Date solved : Thursday, October 02, 2025 at 09:46:43 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 12

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

\[ y = \left (t -1\right ) {\mathrm e}^{t}+c_1 \]

✓ Mathematica. Time used: 0.029 (sec). Leaf size: 15

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

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

✓ Sympy. Time used: 0.078 (sec). Leaf size: 12

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

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