76.1.32 problem 32

Internal problem ID [17331]
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 : 32
Date solved : Tuesday, January 28, 2025 at 10:01:19 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {6-{\mathrm e}^{x}}{3+2 y} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.177 (sec). Leaf size: 19

dsolve([diff(y(x),x)=(6-exp(x))/(3+2*y(x)),y(0) = 0],y(x), singsol=all)
 

\[ y = -\frac {3}{2}+\frac {\sqrt {13-4 \,{\mathrm e}^{x}+24 x}}{2} \]

✓ Solution by Mathematica

Time used: 0.685 (sec). Leaf size: 25

DSolve[{D[y[x],x]==(6-Exp[x])/(3+2*y[x]),{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} \left (\sqrt {24 x-4 e^x+13}-3\right ) \]