73.3.18 problem 4.5 (b)

Internal problem ID [15052]
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 : 4.5 (b)
Date solved : Tuesday, January 28, 2025 at 07:28:49 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=2 x -1+2 y x -y \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 14

dsolve([diff(y(x),x)=2*x-1+2*x*y(x)-y(x),y(0) = 2],y(x), singsol=all)
 

\[ y = -1+3 \,{\mathrm e}^{\left (x -1\right ) x} \]

✓ Solution by Mathematica

Time used: 0.056 (sec). Leaf size: 16

DSolve[{D[y[x],x]==2*x-1+2*x*y[x]-y[x],{y[0]==2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 3 e^{(x-1) x}-1 \]