Internal problem ID [502]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.2. Page 48
Problem number: 24.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {2-{\mathrm e}^{x}}{3+2 y}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.229 (sec). Leaf size: 19
dsolve([diff(y(x),x) = (2-exp(x))/(3+2*y(x)),y(0) = 0],y(x), singsol=all)
\[ y \relax (x ) = -\frac {3}{2}+\frac {\sqrt {13-4 \,{\mathrm e}^{x}+8 x}}{2} \]
✓ Solution by Mathematica
Time used: 0.158 (sec). Leaf size: 25
DSolve[{y'[x] == (2-Exp[x])/(3+2*y[x]),y[0]==0},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (\sqrt {8 x-4 e^x+13}-3\right ) \\ \end{align*}