36.2.13 problem 13

Internal problem ID [6306]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.3, Linear equations. Exercises. page 54
Problem number : 13
Date solved : Sunday, March 30, 2025 at 10:50:14 AM
CAS classification : [_linear]

\begin{align*} y x^{\prime }+2 x&=5 y^{3} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 13

ode:=y*diff(x(y),y)+2*x(y) = 5*y^3; 
dsolve(ode,x(y), singsol=all);
 

\[ x = \frac {y^{5}+c_1}{y^{2}} \]

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 15

ode=y*D[x[y],y]+2*x[y]==5*y^3; 
ic={}; 
DSolve[{ode,ic},x[y],y,IncludeSingularSolutions->True]
 

\[ x(y)\to \frac {y^5+c_1}{y^2} \]

✓ Sympy. Time used: 0.171 (sec). Leaf size: 10

from sympy import * 
y = symbols("y") 
x = Function("x") 
ode = Eq(-5*y**3 + y*Derivative(x(y), y) + 2*x(y),0) 
ics = {} 
dsolve(ode,func=x(y),ics=ics)
 

\[ x{\left (y \right )} = \frac {C_{1} + y^{5}}{y^{2}} \]