89.10.13 problem 13

Internal problem ID [24506]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 4. Additional topics on equations of first order and first degree. Exercises at page 77
Problem number : 13
Date solved : Thursday, October 02, 2025 at 10:43:48 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} 5 x +3 \,{\mathrm e}^{y}+2 x \,{\mathrm e}^{y} y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 20

ode:=5*x+3*exp(y(x))+2*x*exp(y(x))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\ln \left (\frac {\left (x^{{5}/{2}}-c_1 \right )^{2}}{x^{3}}\right )}{2} \]

✓ Mathematica. Time used: 3.694 (sec). Leaf size: 21

ode=( 5*x+3*Exp[y[x]])+2*x*Exp[y[x]]*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \log \left (-x+\frac {c_1}{2 x^{3/2}}\right ) \end{align*}

✓ Sympy. Time used: 0.366 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x*exp(y(x))*Derivative(y(x), x) + 5*x + 3*exp(y(x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \log {\left (\frac {C_{1}}{x^{\frac {3}{2}}} - x \right )} \]