13.1.4 problem Example 6

Internal problem ID [2297]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 1.2. Page 6
Problem number : Example 6
Date solved : Tuesday, March 04, 2025 at 01:53:24 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (1\right )&=2 \end{align*}

✓ Maple. Time used: 0.013 (sec). Leaf size: 17

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

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

✓ Mathematica. Time used: 0.039 (sec). Leaf size: 22

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

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

✓ Sympy. Time used: 0.307 (sec). Leaf size: 17

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

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