13.2.10 problem 11

Internal problem ID [2308]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 1.2. Page 9
Problem number : 11
Date solved : Saturday, March 29, 2025 at 11:53:36 PM
CAS classification : [_separable]

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

With initial conditions

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

✓ Maple. Time used: 0.025 (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: 0.026 (sec). Leaf size: 18

ode=-2*t*y[t]+D[y[t],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: 0.299 (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)
 

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