14.1.11 problem 11

Internal problem ID [2482]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 1. First order differential equations. Section 1.2. Linear equations. Excercises page 9
Problem number : 11
Date solved : Sunday, March 30, 2025 at 12:02:53 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Maple. Time used: 0.021 (sec). Leaf size: 12

ode:=diff(y(t),t)-2*t*y(t) = t; 
ic:=y(0) = 1; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = -\frac {1}{2}+\frac {3 \,{\mathrm e}^{t^{2}}}{2} \]

✓ Mathematica. Time used: 0.031 (sec). Leaf size: 18

ode=D[y[t],t]-2*t*y[t]==t; 
ic={y[0]==1}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \frac {1}{2} \left (3 e^{t^2}-1\right ) \]

✓ Sympy. Time used: 0.301 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-2*t*y(t) - t + Derivative(y(t), t),0) 
ics = {y(0): 1} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {3 e^{t^{2}}}{2} - \frac {1}{2} \]