Internal problem ID [4992]
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: 32.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime }-2 \sqrt {2 x +y+1}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.02 (sec). Leaf size: 56
dsolve(diff(y(x),x)=2*sqrt(2*x+y(x)+1),y(x), singsol=all)
\[ x -\sqrt {2 x +y \relax (x )+1}-\frac {\ln \left (-1+\sqrt {2 x +y \relax (x )+1}\right )}{2}+\frac {\ln \left (\sqrt {2 x +y \relax (x )+1}+1\right )}{2}+\frac {\ln \left (2 x +y \relax (x )\right )}{2}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.097 (sec). Leaf size: 40
DSolve[y'[x]==2*Sqrt[2*x+y[x]+1],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -2 x+\text {ProductLog}\left (-e^{-x-\frac {3}{2}+c_1}\right ) \left (2+\text {ProductLog}\left (-e^{-x-\frac {3}{2}+c_1}\right )\right ) \\ \end{align*}