73.6.3 problem 7.4 (a)

Internal problem ID [15063]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 7. The exact form and general integrating fators. Additional exercises. page 141
Problem number : 7.4 (a)
Date solved : Thursday, March 13, 2025 at 05:33:42 AM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.102 (sec). Leaf size: 71

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

\begin{align*} y &= \frac {-c_{1}^{2} x^{2}+\sqrt {c_{1} x \left (c_{1}^{3} x^{3}+4\right )}}{2 c_{1}^{2} x} \\ y &= \frac {-c_{1}^{2} x^{2}-\sqrt {c_{1} x \left (c_{1}^{3} x^{3}+4\right )}}{2 c_{1}^{2} x} \\ \end{align*}

✓ Mathematica. Time used: 0.123 (sec). Leaf size: 40

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

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {2 K[1]+1}{K[1] (K[1]+1)}dK[1]=-3 \log (x)+c_1,y(x)\right ] \]

✓ Sympy. Time used: 1.365 (sec). Leaf size: 36

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

\[ \left [ y{\left (x \right )} = \frac {x \left (\sqrt {\frac {C_{1}}{x^{3}} + 1} - 1\right )}{2}, \ y{\left (x \right )} = \frac {x \left (- \sqrt {\frac {C_{1}}{x^{3}} + 1} - 1\right )}{2}\right ] \]