60.2.417 problem 995

Internal problem ID [10991]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 995
Date solved : Wednesday, March 05, 2025 at 01:35:40 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*}

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

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

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

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

ode=D[y[x],x] == E^x + (-E^x + y[x])^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to e^x+\frac {1}{-x+c_1} \\ y(x)\to e^x \\ \end{align*}

✓ Sympy. Time used: 0.744 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-(y(x) - exp(x))**2 - exp(x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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