83.8.7 problem 7

Internal problem ID [19062]
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. Misc examples on chapter II at page 25
Problem number : 7
Date solved : Monday, March 31, 2025 at 06:42:54 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

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

✓ Maple. Time used: 0.056 (sec). Leaf size: 19

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

\[ y = {\mathrm e}^{\frac {\left (x -1\right ) {\mathrm e}^{x}-c_1}{x}} \]

✓ Mathematica. Time used: 0.46 (sec). Leaf size: 21

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

\[ y(x)\to e^{\frac {e^x (x-1)+c_1}{x}} \]

✓ Sympy. Time used: 0.924 (sec). Leaf size: 15

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

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