36.3.2 problem 2

Internal problem ID [6323]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.4, Exact equations. Exercises. page 64
Problem number : 2
Date solved : Sunday, March 30, 2025 at 10:51:33 AM
CAS classification : [_linear]

\begin{align*} x^{{10}/{3}}-2 y+x y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 18

ode:=x^(10/3)-2*y(x)+x*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {\left (3 x^{{4}/{3}}-4 c_1 \right ) x^{2}}{4} \]

✓ Mathematica. Time used: 0.035 (sec). Leaf size: 21

ode=(x^(10/3)-2*y[x])+x*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -\frac {3 x^{10/3}}{4}+c_1 x^2 \]

✓ Sympy. Time used: 0.267 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**(10/3) + x*Derivative(y(x), x) - 2*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} x^{2} - \frac {3 x^{\frac {10}{3}}}{4} \]