7.1.2 problem Example 4

Internal problem ID [2295]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 1.2. Page 6
Problem number : Example 4
Date solved : Tuesday, September 30, 2025 at 05:26:03 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }+{\mathrm e}^{t^{2}} y&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.077 (sec). Leaf size: 19

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

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

✓ Mathematica. Time used: 0.041 (sec). Leaf size: 25

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

\begin{align*} y(t)&\to 2 e^{\frac {1}{2} \sqrt {\pi } (\text {erfi}(1)-\text {erfi}(t))} \end{align*}

✓ Sympy. Time used: 0.187 (sec). Leaf size: 27

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

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