67.3.27 problem 4.7 (a)

Internal problem ID [16348]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 4. SEPARABLE FIRST ORDER EQUATIONS. Additional exercises. page 90
Problem number : 4.7 (a)
Date solved : Thursday, October 02, 2025 at 01:22:00 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=y x -4 x \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

ode:=diff(y(x),x) = x*y(x)-4*x; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 24

ode=D[y[x],x]==x*y[x]-4*x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 4+c_1 e^{\frac {x^2}{2}}\\ y(x)&\to 4 \end{align*}

✓ Sympy. Time used: 0.189 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*y(x) + 4*x + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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