29.19.8 problem 521

Internal problem ID [5117]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 19
Problem number : 521
Date solved : Sunday, March 30, 2025 at 06:41:26 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 39

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

\begin{align*} y &= -2-\sqrt {4+\left (-2 x -2 c_1 \right ) a} \\ y &= -2+\sqrt {4+\left (-2 x -2 c_1 \right ) a} \\ \end{align*}

✓ Mathematica. Time used: 0.132 (sec). Leaf size: 50

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

\begin{align*} y(x)\to -2-\sqrt {2} \sqrt {-a x+2+c_1} \\ y(x)\to -2+\sqrt {2} \sqrt {-a x+2+c_1} \\ \end{align*}

✓ Sympy. Time used: 0.364 (sec). Leaf size: 29

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

\[ \left [ y{\left (x \right )} = - \sqrt {C_{1} - 2 a x} - 2, \ y{\left (x \right )} = \sqrt {C_{1} - 2 a x} - 2\right ] \]