Internal problem ID [9329]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 995.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x),G(x)]`], _Riccati]
\[ \boxed {y^{\prime }-\left (y-{\mathrm e}^{x}\right )^{2}={\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve(diff(y(x),x) = (y(x)-exp(x))^2+exp(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {-1+\left (x -c_{1} \right ) {\mathrm e}^{x}}{x -c_{1}} \]
✓ Solution by Mathematica
Time used: 0.307 (sec). Leaf size: 24
DSolve[y'[x] == E^x + (-E^x + y[x])^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^x+\frac {1}{-x+c_1} \\ y(x)\to e^x \\ \end{align*}