Internal problem ID [14222]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number: 61 (a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _Riccati]
\[ \boxed {y^{\prime }-\left (x +y-4\right )^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(diff(y(x),x)=(x+y(x)-4)^2,y(x), singsol=all)
\[ y \left (x \right ) = -x +4-\tan \left (c_{1} -x \right ) \]
✓ Solution by Mathematica
Time used: 0.168 (sec). Leaf size: 41
DSolve[y'[x]==(x+y[x]-4)^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x+\frac {1}{c_1 e^{2 i x}-\frac {i}{2}}+(4-i) \\ y(x)\to -x+(4-i) \\ \end{align*}