76.1.25 problem 25

Internal problem ID [17324]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.1 (Separable equations). Problems at page 44
Problem number : 25
Date solved : Tuesday, January 28, 2025 at 10:00:16 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{-x}-{\mathrm e}^{x}}{3+4 y} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.290 (sec). Leaf size: 29

dsolve([diff(y(x),x)=(exp(-x)-exp(x))/(3+4*y(x)),y(0) = 1],y(x), singsol=all)
 

\[ y = -\frac {3}{4}+\frac {\sqrt {{\mathrm e}^{x} \left (-8-8 \,{\mathrm e}^{2 x}+65 \,{\mathrm e}^{x}\right )}\, {\mathrm e}^{-x}}{4} \]

✓ Solution by Mathematica

Time used: 1.340 (sec). Leaf size: 29

DSolve[{D[y[x],x]==(Exp[-x]-Exp[x])/(3+4*y[x]),{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{4} \left (\sqrt {-8 e^{-x}-8 e^x+65}-3\right ) \]