40.2.22 problem 47

Internal problem ID [6600]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 4. Equations of first order and first degree (Variable separable). Supplemetary problems. Page 22
Problem number : 47
Date solved : Sunday, March 30, 2025 at 11:11:40 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

With initial conditions

\begin{align*} y \left (1\right )&=-1 \end{align*}

✓ Maple. Time used: 0.078 (sec). Leaf size: 18

ode:=x^2+y(x)^2+x*y(x)*diff(y(x),x) = 0; 
ic:=y(1) = -1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = -\frac {\sqrt {-2 x^{4}+6}}{2 x} \]

✓ Mathematica. Time used: 0.226 (sec). Leaf size: 26

ode=(x^2+y[x]^2)+x*y[x]*D[y[x],x]==0; 
ic={y[1]==-1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -\frac {\sqrt {3-x^4}}{\sqrt {2} x} \]

✓ Sympy. Time used: 0.451 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2 + x*y(x)*Derivative(y(x), x) + y(x)**2,0) 
ics = {y(1): -1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - \frac {\sqrt {6 - 2 x^{4}}}{2 x} \]