23.2.308 problem 331

Internal problem ID [5663]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 2. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF SECOND OR HIGHER DEGREE, page 278
Problem number : 331
Date solved : Tuesday, September 30, 2025 at 01:40:40 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.019 (sec). Leaf size: 65

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

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

✓ Mathematica. Time used: 0.284 (sec). Leaf size: 130

ode=(x+2 y[x])(D[y[x],x])^3+3 (x+y[x]) (D[y[x],x])^2+ (2 x+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 (-x-\sqrt {-3 x^2+4 e^{c_1}}\right )\\ y(x)&\to \frac {1}{2} \left (-x+\sqrt {-3 x^2+4 e^{c_1}}\right )\\ y(x)&\to c_1\\ y(x)&\to -x+c_1\\ y(x)&\to \frac {1}{2} \left (-\sqrt {3} \sqrt {-x^2}-x\right )\\ y(x)&\to \frac {1}{2} \left (\sqrt {3} \sqrt {-x^2}-x\right ) \end{align*}

✓ Sympy. Time used: 1.155 (sec). Leaf size: 44

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

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