83.43.16 problem Ex 17 page 23

Internal problem ID [19453]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter II. Equations of first order and first degree
Problem number : Ex 17 page 23
Date solved : Monday, March 31, 2025 at 07:15:17 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} x^{2} y-\left (x^{3}+y^{3}\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.011 (sec). Leaf size: 16

ode:=x^2*y(x)-(x^3+y(x)^3)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\left (\frac {1}{\operatorname {LambertW}\left (c_1 \,x^{3}\right )}\right )}^{{1}/{3}} x \]

✓ Mathematica. Time used: 6.984 (sec). Leaf size: 80

ode=x^2*y[x]-(x^3+y[x]^3)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {x}{\sqrt [3]{W\left (e^{-3 c_1} x^3\right )}} \\ y(x)\to -\frac {\sqrt [3]{-1} x}{\sqrt [3]{W\left (e^{-3 c_1} x^3\right )}} \\ y(x)\to \frac {(-1)^{2/3} x}{\sqrt [3]{W\left (e^{-3 c_1} x^3\right )}} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.804 (sec). Leaf size: 17

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

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