64.6.8 problem 8

Internal problem ID [13279]
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 : Wednesday, March 05, 2025 at 09:33:10 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Riccati]

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

✓ Maple. Time used: 0.017 (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: 0.088 (sec). Leaf size: 38

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]
 

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

✓ Sympy. Time used: 0.275 (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)
 

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