60.2.418 problem 995

Internal problem ID [11005]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 995
Date solved : Monday, January 27, 2025 at 10:40:13 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`], _Riccati]

\begin{align*} y^{\prime }&=\left (y-{\mathrm e}^{x}\right )^{2}+{\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 22

dsolve(diff(y(x),x) = (y(x)-exp(x))^2+exp(x),y(x), singsol=all)
 

\[ y = \frac {-1+\left (x -c_{1} \right ) {\mathrm e}^{x}}{x -c_{1}} \]

✓ Solution by Mathematica

Time used: 0.302 (sec). Leaf size: 24

DSolve[D[y[x],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*}