15.8.36 problem 38

Internal problem ID [3039]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 12, page 46
Problem number : 38
Date solved : Tuesday, March 04, 2025 at 03:47:27 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} x y^{\prime }-5 y-x \sqrt {y}&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 17

ode:=x*diff(y(x),x)-5*y(x)-x*y(x)^(1/2) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \sqrt {y}+\frac {x}{3}-x^{{5}/{2}} c_{1} = 0 \]

✓ Mathematica. Time used: 0.178 (sec). Leaf size: 25

ode=x*D[y[x],x]-(5*y[x]+x*Sqrt[y[x]])==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{9} x^2 \left (1-3 c_1 x^{3/2}\right ){}^2 \]

✓ Sympy. Time used: 0.274 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*sqrt(y(x)) + x*Derivative(y(x), x) - 5*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1}^{2} x^{5} - \frac {2 C_{1} x^{\frac {7}{2}}}{3} + \frac {x^{2}}{9} \]