73.2.8 problem 3.4 h

Internal problem ID [15031]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 3. Some basics about First order equations. Additional exercises. page 63
Problem number : 3.4 h
Date solved : Tuesday, January 28, 2025 at 07:28:01 AM
CAS classification : [_separable]

\begin{align*} \left (y-2\right ) y^{\prime }&=x -3 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 39

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

\begin{align*} y &= 2-\sqrt {x^{2}+2 c_{1} -6 x +4} \\ y &= 2+\sqrt {x^{2}+2 c_{1} -6 x +4} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.112 (sec). Leaf size: 47

DSolve[(y[x]-2)*D[y[x],x]==x-3,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to 2-\sqrt {x^2-6 x+4+2 c_1} \\ y(x)\to 2+\sqrt {x^2-6 x+4+2 c_1} \\ \end{align*}