62.5.2 problem Ex 2

Internal problem ID [12746]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter 2, differential equations of the first order and the first degree. Article 12. Page 18
Problem number : Ex 2
Date solved : Monday, March 31, 2025 at 07:01:38 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} 2 y+3 x y^{2}+\left (x +2 x^{2} y\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.012 (sec). Leaf size: 45

ode:=2*y(x)+3*x*y(x)^2+(x+2*x^2*y(x))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.702 (sec). Leaf size: 69

ode=(2*y[x]+3*x*y[x]^2)+(x+2*x^2*y[x])*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -\frac {x^{3/2}+\sqrt {x^2 (x+4 c_1)}}{2 x^{5/2}} \\ y(x)\to \frac {-x^{3/2}+\sqrt {x^2 (x+4 c_1)}}{2 x^{5/2}} \\ \end{align*}

✓ Sympy. Time used: 0.929 (sec). Leaf size: 32

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

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