47.1.33 problem 33

Internal problem ID [7414]
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
Date solved : Monday, January 27, 2025 at 02:53:31 PM
CAS classification : [[_homogeneous, `class C`], _Riccati]

\begin{align*} y^{\prime }&=\left (x +y+1\right )^{2} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 17

dsolve(diff(y(x),x)=(x+y(x)+1)^2,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.611 (sec). Leaf size: 15

DSolve[D[y[x],x]==(x+y[x]+1)^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -x+\tan (x+c_1)-1 \]