80.5.6 problem 8

Internal problem ID [18564]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter IV. Methods of solution: First order equations. section 32. Problems at page 89
Problem number : 8
Date solved : Tuesday, January 28, 2025 at 12:00:12 PM
CAS classification : [[_homogeneous, `class C`], _Riccati]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 0.509 (sec). Leaf size: 14

DSolve[D[y[x],x]==(x+y[x])^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -x+\tan (x+c_1) \]