83.43.6 problem Ex 7 page 9

Internal problem ID [19443]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter II. Equations of first order and first degree
Problem number : Ex 7 page 9
Date solved : Monday, March 31, 2025 at 07:14:38 PM
CAS classification : [_separable]

\begin{align*} 1+y^{2}-x y y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 27

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

\begin{align*} y &= \sqrt {c_1 \,x^{2}-1} \\ y &= -\sqrt {c_1 \,x^{2}-1} \\ \end{align*}

✓ Mathematica. Time used: 0.401 (sec). Leaf size: 57

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

\begin{align*} y(x)\to -\sqrt {-1+e^{2 c_1} x^2} \\ y(x)\to \sqrt {-1+e^{2 c_1} x^2} \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}

✓ Sympy. Time used: 0.463 (sec). Leaf size: 26

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

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