88.6.11 problem 11

Internal problem ID [23993]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Exercise at page 38
Problem number : 11
Date solved : Thursday, October 02, 2025 at 09:49:59 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{\prime }&=\frac {2 x^{2}+2 y^{2}-3 y x}{y x} \end{align*}

✓ Maple. Time used: 0.065 (sec). Leaf size: 44

ode:=diff(y(x),x) = (2*x^2+2*y(x)^2-3*x*y(x))/x/y(x); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -\frac {\left (-c_1 x +\sqrt {c_1 x \left (c_1 x +4\right )}-4\right ) x}{2} \\ y &= \frac {\left (c_1 x +\sqrt {c_1 x \left (c_1 x +4\right )}+4\right ) x}{2} \\ \end{align*}

✓ Mathematica. Time used: 1.129 (sec). Leaf size: 88

ode=D[y[x],{x,1}]==( 2*x^2+2*y[x]^2-3*x*y[x] )/( x*y[x] ); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 1.605 (sec). Leaf size: 61

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - (2*x**2 - 3*x*y(x) + 2*y(x)**2)/(x*y(x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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