67.4.19 problem 5.2 (i)

Internal problem ID [16388]
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 (i)
Date solved : Thursday, October 02, 2025 at 01:27:27 PM
CAS classification : [_linear]

\begin{align*} x y^{\prime }+\left (2+5 x \right ) y&=\frac {20}{x} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

ode:=x*diff(y(x),x)+(5*x+2)*y(x) = 20/x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{-5 x} c_1 +4}{x^{2}} \]

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 12

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

\begin{align*} y(x)&\to (x+c_1) \cos (x) \end{align*}

✓ Sympy. Time used: 0.186 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), x) + (5*x + 2)*y(x) - 20/x,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} e^{- 5 x} + 4}{x^{2}} \]