32.6.17 problem Exercise 12.17, page 103

Internal problem ID [5882]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous Methods
Problem number : Exercise 12.17, page 103
Date solved : Monday, January 27, 2025 at 01:23:41 PM
CAS classification : [[_homogeneous, `class C`], _Riccati]

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

✓ Solution by Maple

Time used: 0.007 (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: 0.546 (sec). Leaf size: 14

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

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