83.3.2 problem 2

Internal problem ID [18987]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Exercise II (B) at page 9
Problem number : 2
Date solved : Monday, March 31, 2025 at 06:28:39 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 21

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

\[ y = -\ln \left (3\right )+\ln \left (x^{3}+3 \,{\mathrm e}^{x}+3 c_1 \right ) \]

✓ Mathematica. Time used: 1.077 (sec). Leaf size: 19

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

\[ y(x)\to \log \left (\frac {x^3}{3}+e^x+c_1\right ) \]

✓ Sympy. Time used: 0.225 (sec). Leaf size: 14

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

\[ y{\left (x \right )} = \log {\left (C_{1} + \frac {x^{3}}{3} + e^{x} \right )} \]