23.1.284 problem 278

Internal problem ID [4891]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 278
Date solved : Tuesday, September 30, 2025 at 08:54:25 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} x^{2} y^{\prime }+x y+\sqrt {y}&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 19

ode:=x^2*diff(y(x),x)+x*y(x)+y(x)^(1/2) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \sqrt {y}-\frac {1}{x}-\frac {c_1}{\sqrt {x}} = 0 \]

✓ Mathematica. Time used: 0.092 (sec). Leaf size: 21

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

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

✓ Sympy. Time used: 0.156 (sec). Leaf size: 20

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

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