10.5.16 problem 21

Internal problem ID [1208]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.6. Page 100
Problem number : 21
Date solved : Saturday, March 29, 2025 at 10:47:22 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

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

✓ Maple. Time used: 0.021 (sec). Leaf size: 30

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

\[ x +\frac {\left (-y^{2}+2 y-2\right ) {\mathrm e}^{y}-c_1}{y^{2}} = 0 \]

✓ Mathematica. Time used: 0.239 (sec). Leaf size: 32

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

\[ \text {Solve}\left [x=\frac {e^{y(x)} \left (y(x)^2-2 y(x)+2\right )}{y(x)^2}+\frac {c_1}{y(x)^2},y(x)\right ] \]

✓ Sympy. Time used: 0.882 (sec). Leaf size: 26

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

\[ C_{1} + x y^{2}{\left (x \right )} - \left (y^{2}{\left (x \right )} - 2 y{\left (x \right )} + 2\right ) e^{y{\left (x \right )}} = 0 \]