34.2.12 problem 37

Internal problem ID [7877]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 4. Equations of first order and first degree (Variable separable). Supplemetary problems. Page 22
Problem number : 37
Date solved : Tuesday, September 30, 2025 at 05:07:40 PM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.012 (sec). Leaf size: 51

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

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

✓ Mathematica. Time used: 0.251 (sec). Leaf size: 99

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

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

✓ Sympy. Time used: 0.768 (sec). Leaf size: 36

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

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