10.5.25 problem 32

Internal problem ID [1217]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.6. Page 100
Problem number : 32
Date solved : Saturday, March 29, 2025 at 10:47:48 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.016 (sec). Leaf size: 59

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

\begin{align*} y &= \frac {-c_1 \,x^{2}-\sqrt {x^{4} c_1^{2}+1}}{c_1 x} \\ y &= \frac {-c_1 \,x^{2}+\sqrt {x^{4} c_1^{2}+1}}{c_1 x} \\ \end{align*}

✓ Mathematica. Time used: 0.643 (sec). Leaf size: 93

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

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

✓ Sympy. Time used: 1.264 (sec). Leaf size: 29

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

\[ \left [ y{\left (x \right )} = - x - \frac {\sqrt {C_{1} + x^{4}}}{x}, \ y{\left (x \right )} = - x + \frac {\sqrt {C_{1} + x^{4}}}{x}\right ] \]