14.1.14 problem 14

Internal problem ID [2485]
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 : 14
Date solved : Sunday, March 30, 2025 at 12:03:01 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }-2 t y&=1 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.056 (sec). Leaf size: 18

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

\[ y = \frac {\left (\sqrt {\pi }\, \operatorname {erf}\left (t \right )+2\right ) {\mathrm e}^{t^{2}}}{2} \]

✓ Mathematica. Time used: 0.029 (sec). Leaf size: 24

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

\[ y(t)\to \frac {1}{2} e^{t^2} \left (\sqrt {\pi } \text {erf}(t)+2\right ) \]

✓ Sympy. Time used: 0.314 (sec). Leaf size: 19

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

\[ y{\left (t \right )} = \left (\frac {\sqrt {\pi } \operatorname {erf}{\left (t \right )}}{2} + 1\right ) e^{t^{2}} \]