40.4.5 problem 19 (f)

Internal problem ID [6645]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 6. Equations of first order and first degree (Linear equations). Supplemetary problems. Page 39
Problem number : 19 (f)
Date solved : Wednesday, March 05, 2025 at 01:34:24 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Bernoulli]

\begin{align*} y^{\prime }+y&=y^{2} {\mathrm e}^{x} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 16

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

\[ y = \frac {{\mathrm e}^{-x}}{-x +c_1} \]

✓ Mathematica. Time used: 0.209 (sec). Leaf size: 25

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

\begin{align*} y(x)\to -\frac {e^{-x}}{x-c_1} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.216 (sec). Leaf size: 10

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

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