83.4.14 problem 14

Internal problem ID [19015]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Exercise II (C) at page 12
Problem number : 14
Date solved : Monday, March 31, 2025 at 06:32:49 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

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

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

\[ y = \frac {x^{{3}/{2}}}{c_1 x +\sqrt {x}} \]

✓ Mathematica. Time used: 0.128 (sec). Leaf size: 24

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

\begin{align*} y(x)\to \frac {x}{1+c_1 \sqrt {x}} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.203 (sec). Leaf size: 12

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

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