Internal problem ID [4030]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-\left (x +y\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 16
dsolve(diff(y(x),x)=(x+y(x))^2,y(x), singsol=all)
\[ y \relax (x ) = -x -\tan \left (c_{1}-x \right ) \]
✓ Solution by Mathematica
Time used: 0.464 (sec). Leaf size: 14
DSolve[y'[x]==(x+y[x])^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x+\tan (x+c_1) \\ \end{align*}