10.2.18 problem 18

Internal problem ID [1146]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.2. Page 48
Problem number : 18
Date solved : Monday, January 27, 2025 at 04:35:49 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: 0.217 (sec). Leaf size: 29

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

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

✓ Solution by Mathematica

Time used: 1.249 (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]
 

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