36.1.30 problem 28

Internal problem ID [6285]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.2, Separable Equations. Exercises. page 46
Problem number : 28
Date solved : Sunday, March 30, 2025 at 10:49:08 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=2 y-2 t y \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.030 (sec). Leaf size: 13

ode:=diff(y(t),t) = 2*y(t)-2*t*y(t); 
ic:=y(0) = 3; 
dsolve([ode,ic],y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 15

ode=D[y[t],t]==2*y[t]-2*t*y[t]; 
ic={y[0]==3}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to 3 e^{-((t-2) t)} \]

✓ Sympy. Time used: 0.283 (sec). Leaf size: 10

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(2*t*y(t) - 2*y(t) + Derivative(y(t), t),0) 
ics = {y(0): 3} 
dsolve(ode,func=y(t),ics=ics)
 

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