67.3.28 problem 4.7 (b)

Internal problem ID [16349]
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 (b)
Date solved : Thursday, October 02, 2025 at 01:22:02 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=y x -3 x -2 y+6 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

ode:=diff(y(x),x) = x*y(x)-3*x-2*y(x)+6; 
dsolve(ode,y(x), singsol=all);
 

\[ y = 3+{\mathrm e}^{\frac {x \left (x -4\right )}{2}} c_1 \]

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 25

ode=D[y[x],x]==x*y[x]-3*x-2*y[x]+6; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 3+c_1 e^{\frac {1}{2} (x-4) x}\\ y(x)&\to 3 \end{align*}

✓ Sympy. Time used: 0.201 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*y(x) + 3*x + 2*y(x) + Derivative(y(x), x) - 6,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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