Internal problem ID [4993]
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]
Solve \begin {gather*} \boxed {y^{\prime }-\left (y+x +1\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 17
dsolve(diff(y(x),x)=(x+y(x)+1)^2,y(x), singsol=all)
\[ y \relax (x ) = -x -1-\tan \left (c_{1}-x \right ) \]
✓ Solution by Mathematica
Time used: 0.488 (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*}