83.5.19 problem 19

Internal problem ID [19043]
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 (D) at page 16
Problem number : 19
Date solved : Monday, March 31, 2025 at 06:36:20 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: 0.002 (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);
 

\[ y = \frac {{\mathrm e}^{x}}{-x^{2}+c_1} \]

✓ Mathematica. Time used: 0.277 (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: 0.212 (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)
 

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