74.4.64 problem 61 (a)

Internal problem ID [15957]
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)
Date solved : Tuesday, January 28, 2025 at 08:24:40 AM
CAS classification : [[_homogeneous, `class C`], _Riccati]

\begin{align*} y^{\prime }&=\left (x +y-4\right )^{2} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 17

dsolve(diff(y(x),x)=(x+y(x)-4)^2,y(x), singsol=all)
 

\[ y = -x +4-\tan \left (-x +c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.165 (sec). Leaf size: 41

DSolve[D[y[x],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*}