Internal problem ID [13400]
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]
\[ \boxed {y^{\prime }-\left (-y+3+x \right )^{2}=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 29
dsolve(diff(y(x),x)=(x-y(x)+3)^2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} \left (x +2\right ) {\mathrm e}^{2 x}-x -4}{-1+{\mathrm e}^{2 x} c_{1}} \]
✓ 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*}