85.33.18 problem 18

Internal problem ID [22641]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 65
Problem number : 18
Date solved : Thursday, October 02, 2025 at 08:57:18 PM
CAS classification : [_rational, _Bernoulli]

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

With initial conditions

\begin{align*} y \left (0\right )&=2 \\ \end{align*}

✓ Maple. Time used: 0.062 (sec). Leaf size: 22

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

\[ y = \sqrt {-x^{2}+6 \,{\mathrm e}^{-x}+2 x -2} \]

✓ Mathematica. Time used: 4.692 (sec). Leaf size: 26

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

\begin{align*} y(x)&\to \sqrt {-x^2+2 x+6 e^{-x}-2} \end{align*}

✓ Sympy. Time used: 0.388 (sec). Leaf size: 19

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

\[ y{\left (x \right )} = \sqrt {- x^{2} + 2 x - 2 + 6 e^{- x}} \]