40.2.16 problem 41

Internal problem ID [6594]
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 : 41
Date solved : Sunday, March 30, 2025 at 11:11:11 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 39

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

\begin{align*} y &= -\frac {\sqrt {2 x^{4}+4 c_1}}{2 x} \\ y &= \frac {\sqrt {2 x^{4}+4 c_1}}{2 x} \\ \end{align*}

✓ Mathematica. Time used: 0.214 (sec). Leaf size: 46

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

\begin{align*} y(x)\to -\frac {\sqrt {\frac {x^4}{2}+c_1}}{x} \\ y(x)\to \frac {\sqrt {\frac {x^4}{2}+c_1}}{x} \\ \end{align*}

✓ Sympy. Time used: 0.413 (sec). Leaf size: 32

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 = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \frac {\sqrt {C_{1} + 2 x^{4}}}{2 x}, \ y{\left (x \right )} = \frac {\sqrt {C_{1} + 2 x^{4}}}{2 x}\right ] \]