7.5.15 problem 15

Internal problem ID [119]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.6 (substitution and exact equations). Problems at page 72
Problem number : 15
Date solved : Tuesday, March 04, 2025 at 10:48:38 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.035 (sec). Leaf size: 59

ode:=x*(x+y(x))*diff(y(x),x)+y(x)*(3*x+y(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: 0.708 (sec). Leaf size: 93

ode=x*(x+y[x])*D[y[x],x]+y[x]*(3*x+y[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: 1.284 (sec). Leaf size: 29

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

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