67.1.1 problem Problem 1(a)

Internal problem ID [13877]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 2, First Order Equations. Problems page 149
Problem number : Problem 1(a)
Date solved : Monday, March 31, 2025 at 08:15:57 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=y \,{\mathrm e}^{x +y} \left (x^{2}+1\right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 20

ode:=diff(y(x),x) = y(x)*exp(x+y(x))*(x^2+1); 
dsolve(ode,y(x), singsol=all);
 

\[ \left (x^{2}-2 x +3\right ) {\mathrm e}^{x}+\operatorname {Ei}_{1}\left (y\right )+c_1 = 0 \]

✓ Mathematica. Time used: 0.543 (sec). Leaf size: 32

ode=D[y[x],x]==y[x]*Exp[x+y[x]]*(x^2+1); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \text {InverseFunction}[\operatorname {ExpIntegralEi}(-\text {$\#$1})\&]\left [e^x \left (x^2-2 x+3\right )+c_1\right ] \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.599 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-(x**2 + 1)*y(x)*exp(x + y(x)) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \operatorname {Ei}{\left (e^{i \pi } y{\left (x \right )} \right )} = C_{1} + \left (x^{2} - 2 x + 3\right ) e^{x} \]