73.3.27 problem 4.7 (a)

Internal problem ID [15061]
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 : Tuesday, January 28, 2025 at 07:29:10 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 14

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

\[ y = 4+{\mathrm e}^{\frac {x^{2}}{2}} c_{1} \]

✓ Solution by Mathematica

Time used: 0.049 (sec). Leaf size: 24

DSolve[D[y[x],x]==x*y[x]-4*x,y[x],x,IncludeSingularSolutions -> True]
 

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