82.6.5 problem Ex. 5

Internal problem ID [18667]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter II. Equations of the first order and of the first degree. Exercises at page 22
Problem number : Ex. 5
Date solved : Thursday, March 13, 2025 at 12:31:48 PM
CAS classification : [_Bernoulli]

\begin{align*} y \left (2 x y+{\mathrm e}^{x}\right )-{\mathrm e}^{x} y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 16

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

\[ y \left (x \right ) = \frac {{\mathrm e}^{x}}{-x^{2}+c_{1}} \]

✓ Mathematica. Time used: 0.306 (sec). Leaf size: 25

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

\begin{align*} y(x)\to -\frac {e^x}{x^2-c_1} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.219 (sec). Leaf size: 10

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

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