Internal problem ID [13080]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 6. Simplifying through simplifiction. Additional exercises. page 114
Problem number: 6.7 (m).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _Riccati]
\[ \boxed {y^{\prime }-\left (x -y+3\right )^{2}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 34
dsolve(diff(y(x),x)=(x-y(x)+3)^2,y(x), singsol=all)
\[ y = \frac {x \,{\mathrm e}^{2 x} c_{1} +2 \,{\mathrm e}^{2 x} c_{1} -x -4}{{\mathrm e}^{2 x} c_{1} -1} \]
✓ Solution by Mathematica
Time used: 0.163 (sec). Leaf size: 29
DSolve[y'[x]==(x-y[x]+3)^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x+\frac {1}{\frac {1}{2}+c_1 e^{2 x}}+2 y(x)\to x+2 \end{align*}