67.4.15 problem 5.2 (e)

Internal problem ID [16384]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 5. LINEAR FIRST ORDER EQUATIONS. Additional exercises. page 103
Problem number : 5.2 (e)
Date solved : Thursday, October 02, 2025 at 01:27:19 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 17

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

\begin{align*} y(x)&\to \frac {2 x^5+c_1}{x^3} \end{align*}

✓ Sympy. Time used: 0.101 (sec). Leaf size: 12

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

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