83.3.6 problem 6

Internal problem ID [18983]
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 : 6
Date solved : Thursday, March 13, 2025 at 01:16:36 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 23

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

\[ y \left (x \right ) = \ln \left (3\right )+\ln \left (-\frac {1}{x^{3}+3 \,{\mathrm e}^{x}+3 c_{1}}\right ) \]

✓ Mathematica. Time used: 1.053 (sec). Leaf size: 25

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: 0.232 (sec). Leaf size: 20

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)
 

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