73.3.8 problem 4.3 (h)

Internal problem ID [15042]
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 : 4.3 (h)
Date solved : Tuesday, January 28, 2025 at 07:28:21 AM
CAS classification : [_separable]

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

✓ Solution by Maple

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

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

\[ y = 3+{\mathrm e}^{\frac {x \left (x -4\right )}{2}} c_{1} \]

✓ Solution by Mathematica

Time used: 0.159 (sec). Leaf size: 25

DSolve[D[y[x],x]==x*y[x]-3*x-2*y[x]+6,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*}