58.6.8 problem 8

Internal problem ID [14639]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, Miscellaneous Review. Exercises page 60
Problem number : 8
Date solved : Thursday, October 02, 2025 at 09:45:13 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Riccati]

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

✓ Maple. Time used: 0.074 (sec). Leaf size: 49

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

\begin{align*} y &= -\frac {\left (c_1 x -\sqrt {c_1 x}-2\right ) x}{c_1 x -1} \\ y &= -\frac {\left (c_1 x +\sqrt {c_1 x}-2\right ) x}{c_1 x -1} \\ \end{align*}

✓ Mathematica. Time used: 1.896 (sec). Leaf size: 47

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

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

✓ Sympy. Time used: 0.164 (sec). Leaf size: 24

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

\[ y{\left (x \right )} = \frac {2 C_{1} x^{\frac {7}{2}} - x^{4}}{- C_{1} x^{\frac {5}{2}} + x^{3}} \]