29.15.1 problem 409

Internal problem ID [5007]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 15
Problem number : 409
Date solved : Tuesday, March 04, 2025 at 07:42:22 PM
CAS classification : [_quadrature]

\begin{align*} X^{{2}/{3}} y^{\prime }&=Y^{{2}/{3}} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 14

ode:=X^(2/3)*diff(y(x),x) = Y^(2/3); 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = \frac {Y^{{2}/{3}} x}{X^{{2}/{3}}}+c_{1} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 20

ode=X^(2/3) D[y[x],x]== Y^(2/3); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {x Y^{2/3}}{X^{2/3}}+c_1 \]

✓ Sympy. Time used: 0.150 (sec). Leaf size: 15

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

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