73.5.25 problem 6.7 (m)

Internal problem ID [15136]
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)
Date solved : Tuesday, January 28, 2025 at 07:36:22 AM
CAS classification : [[_homogeneous, `class C`], _Riccati]

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

✓ Solution by Maple

Time used: 0.076 (sec). Leaf size: 31

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

\[ y = \frac {\left (-x -2\right ) {\mathrm e}^{2 x}+\left (x +4\right ) c_{1}}{-{\mathrm e}^{2 x}+c_{1}} \]

✓ Solution by Mathematica

Time used: 0.184 (sec). Leaf size: 29

DSolve[D[y[x],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*}