Internal problem ID [12975]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (y-2\right ) y^{\prime }=x -3} \]
✓ Solution by Maple
Time used: 0.0 (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)*y'[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*}