87.6.1 problem 1

Internal problem ID [23318]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 1. Elementary methods. First order differential equations. Exercise at page 53
Problem number : 1
Date solved : Thursday, October 02, 2025 at 09:31:53 PM
CAS classification : [_linear]

\begin{align*} 5 x -y+3 x y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.000 (sec). Leaf size: 13

ode:=5*x-y(x)+3*x*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {5 x}{2}+x^{{1}/{3}} c_1 \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 19

ode=(5*x-y[x])+(3*x)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {5 x}{2}+c_1 \sqrt [3]{x} \end{align*}

✓ Sympy. Time used: 0.151 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*x*Derivative(y(x), x) + 5*x - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} \sqrt [3]{x} - \frac {5 x}{2} \]