Internal problem ID [4992]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 1. First order differential equations. Section 1.1 Separable equations problems. page
7
Problem number: 33.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _Riccati]
\[ \boxed {y^{\prime }-\left (y+x +1\right )^{2}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve(diff(y(x),x)=(x+y(x)+1)^2,y(x), singsol=all)
\[ y \left (x \right ) = -x -1-\tan \left (-x +c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.483 (sec). Leaf size: 15
DSolve[y'[x]==(x+y[x]+1)^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x+\tan (x+c_1)-1 \\ \end{align*}