83.6.2 problem 2

Internal problem ID [19047]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Exercise II (E) at page 19
Problem number : 2
Date solved : Monday, March 31, 2025 at 06:36:45 PM
CAS classification : [_exact, _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} 1+4 x y+2 y^{2}+\left (1+4 x y+2 x^{2}\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 69

ode:=1+4*x*y(x)+2*y(x)^2+(1+4*x*y(x)+2*x^2)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {-2 x^{2}-1+\sqrt {4 x^{4}-8 c_1 x -4 x^{2}+1}}{4 x} \\ y &= \frac {-2 x^{2}-1-\sqrt {4 x^{4}-8 c_1 x -4 x^{2}+1}}{4 x} \\ \end{align*}

✓ Mathematica. Time used: 0.621 (sec). Leaf size: 79

ode=(1+4*x*y[x]+2*y[x]^2)+(1+4*x*y[x]+2*x^2)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -\frac {2 x^2+\sqrt {4 x^4-4 x^2+16 c_1 x+1}+1}{4 x} \\ y(x)\to \frac {-2 x^2+\sqrt {4 x^4-4 x^2+16 c_1 x+1}-1}{4 x} \\ \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x*y(x) + (2*x**2 + 4*x*y(x) + 1)*Derivative(y(x), x) + 2*y(x)**2 + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out