13.1.2 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 : Monday, January 27, 2025 at 05:44:52 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*}

✓ Solution by Maple

Time used: 0.073 (sec). Leaf size: 19

dsolve([diff(y(t),t)+exp(t^2)*y(t)=0,y(1) = 2],y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.068 (sec). Leaf size: 25

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

\[ y(t)\to 2 e^{\frac {1}{2} \sqrt {\pi } (\text {erfi}(1)-\text {erfi}(t))} \]