47.2.36 problem 34

Internal problem ID [7452]
Book : Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section : Chapter 1. First order differential equations. Section 1.2 Homogeneous equations problems. page 12
Problem number : 34
Date solved : Monday, January 27, 2025 at 03:00:28 PM
CAS classification : [[_homogeneous, `class C`], _rational]

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

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 25

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

\[ y = -2-\tan \left (\operatorname {RootOf}\left (-2 \textit {\_Z} +\ln \left (\tan \left (\textit {\_Z} \right )\right )+\ln \left (x -1\right )+c_{1} \right )\right ) \left (x -1\right ) \]

✓ Solution by Mathematica

Time used: 0.166 (sec). Leaf size: 27

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

\[ \text {Solve}\left [2 \arctan \left (\frac {1-x}{y(x)+2}\right )+\log (y(x)+2)=c_1,y(x)\right ] \]