28.1.36 problem 36

Internal problem ID [4342]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 36
Date solved : Sunday, March 30, 2025 at 03:06:03 AM
CAS classification : [_rational, _Bernoulli]

\begin{align*} 2+y^{2}+2 x +2 y y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 33

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

\begin{align*} y &= \sqrt {{\mathrm e}^{-x} c_1 -2 x} \\ y &= -\sqrt {{\mathrm e}^{-x} c_1 -2 x} \\ \end{align*}

✓ Mathematica. Time used: 3.623 (sec). Leaf size: 43

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

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

✓ Sympy. Time used: 0.478 (sec). Leaf size: 29

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

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