83.45.2 problem Ex 2 page 52

Internal problem ID [19474]
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 IV. Equations of the first order but not of the first degree
Problem number : Ex 2 page 52
Date solved : Monday, March 31, 2025 at 07:19:43 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

\begin{align*} x^{2} \left ({y^{\prime }}^{2}-y^{2}\right )+y^{2}&=x^{4}+2 x y y^{\prime } \end{align*}

✓ Maple. Time used: 0.750 (sec). Leaf size: 56

ode:=x^2*(diff(y(x),x)^2-y(x)^2)+y(x)^2 = x^4+2*x*y(x)*diff(y(x),x); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -i x \\ y &= i x \\ y &= \frac {x \left (c_1^{2} {\mathrm e}^{-x}-{\mathrm e}^{x}\right )}{2 c_1} \\ y &= -\frac {x \left (-c_1^{2} {\mathrm e}^{x}+{\mathrm e}^{-x}\right )}{2 c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.143 (sec). Leaf size: 26

ode=x^2*(D[y[x],x]^2-y[x]^2)+y[x]^2==x^4+2*x*y[x]*D[y[x],x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -x \sinh (x-c_1) \\ y(x)\to x \sinh (x+c_1) \\ \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**4 + x**2*(-y(x)**2 + Derivative(y(x), x)**2) - 2*x*y(x)*Derivative(y(x), x) + y(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out