Internal problem ID [1022]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable
Equations. Section 2.4 Page 68
Problem number: 47.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-y^{2} {\mathrm e}^{-x}-4 y-2 \,{\mathrm e}^{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.025 (sec). Leaf size: 22
dsolve(diff(y(x),x)=y(x)^2*exp(-x)+4*y(x)+2*exp(x),y(x), singsol=all)
\[ y \relax (x ) = -\frac {2 \,{\mathrm e}^{x} \left (c_{1} {\mathrm e}^{x}-1\right )}{-2+c_{1} {\mathrm e}^{x}} \]
✓ Solution by Mathematica
Time used: 0.281 (sec). Leaf size: 30
DSolve[y'[x]==y[x]^2*Exp[-x]+4*y[x]+2*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -2 e^x+\frac {1}{e^{-x}+c_1} \\ y(x)\to -2 e^x \\ \end{align*}