Internal problem ID [5030]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational]
\[ \boxed {y^{\prime }-\frac {2 \left (y+2\right )^{2}}{\left (y+x +1\right )^{2}}=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 25
dsolve(diff(y(x),x)=2*((y(x)+2)/(x+y(x)+1))^2,y(x), singsol=all)
\[ y \left (x \right ) = -2-\tan \left (\operatorname {RootOf}\left (-2 \textit {\_Z} +\ln \left (\tan \left (\textit {\_Z} \right )\right )+\ln \left (x -1\right )+c_{1} \right )\right ) \left (x -1\right ) \]
✓ Solution by Mathematica
Time used: 0.129 (sec). Leaf size: 27
DSolve[y'[x]==2*((y[x]+2)/(x+y[x]+1))^2,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [2 \arctan \left (\frac {1-x}{y(x)+2}\right )+\log (y(x)+2)=c_1,y(x)\right ] \]