10.2.24 problem 24

Internal problem ID [1152]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.2. Page 48
Problem number : 24
Date solved : Monday, January 27, 2025 at 04:36:47 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {2-{\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: 0.157 (sec). Leaf size: 19

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

\[ y = -\frac {3}{2}+\frac {\sqrt {13-4 \,{\mathrm e}^{x}+8 x}}{2} \]

✓ Solution by Mathematica

Time used: 0.632 (sec). Leaf size: 25

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

\[ y(x)\to \frac {1}{2} \left (\sqrt {8 x-4 e^x+13}-3\right ) \]