14.4.13 problem 13

Internal problem ID [2531]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 1. First order differential equations. Section 1.10. Existence-uniqueness theorem. Excercises page 80
Problem number : 13
Date solved : Monday, January 27, 2025 at 05:59:16 AM
CAS classification : [`y=_G(x,y')`]

\begin{align*} y^{\prime }&=\left (4 y+{\mathrm e}^{-t^{2}}\right ) {\mathrm e}^{2 y} \end{align*}

With initial conditions

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

✗ Solution by Maple

dsolve([diff(y(t),t)=(4*y(t)+exp(-t^2))*exp(2*y(t)),y(0) = 0],y(t), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[{D[y[t],t]==(4*y[t]+Exp[-t^2])*Exp[2*y[t]],{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
 

Not solved