8.5.31 problem 31

Internal problem ID [759]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.6, Substitution methods and exact equations. Page 74
Problem number : 31
Date solved : Saturday, March 29, 2025 at 10:20:05 PM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.017 (sec). Leaf size: 53

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

\begin{align*} y &= \frac {-3 c_1 x -\sqrt {5 x^{2} c_1^{2}+4}}{2 c_1} \\ y &= \frac {-3 c_1 x +\sqrt {5 x^{2} c_1^{2}+4}}{2 c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.401 (sec). Leaf size: 110

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

\begin{align*} y(x)\to \frac {1}{2} \left (-3 x-\sqrt {5 x^2+4 e^{c_1}}\right ) \\ y(x)\to \frac {1}{2} \left (-3 x+\sqrt {5 x^2+4 e^{c_1}}\right ) \\ y(x)\to \frac {1}{2} \left (-\sqrt {5} \sqrt {x^2}-3 x\right ) \\ y(x)\to \frac {1}{2} \left (\sqrt {5} \sqrt {x^2}-3 x\right ) \\ \end{align*}

✓ Sympy. Time used: 1.229 (sec). Leaf size: 36

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

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