Internal problem ID [15118]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 9. The Riccati equation. Exercises page 75
Problem number: 232.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x),G(x)]`], _Riccati]
\[ \boxed {y^{\prime } {\mathrm e}^{-x}+y^{2}-2 y \,{\mathrm e}^{x}=1-{\mathrm e}^{2 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(y(x),x)*exp(-x)+y(x)^2-2*y(x)*exp(x)=1-exp(2*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{x}+{\mathrm e}^{2 x} c_{1} +c_{1}}{{\mathrm e}^{x} c_{1} +1} \]
✓ Solution by Mathematica
Time used: 0.311 (sec). Leaf size: 24
DSolve[y'[x]*Exp[-x]+y[x]^2-2*y[x]*Exp[x]==1-Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^x+\frac {1}{e^x+c_1} \\ y(x)\to e^x \\ \end{align*}