47.1.32 problem 32

Internal problem ID [7413]
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
Date solved : Monday, January 27, 2025 at 02:53:29 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} y^{\prime }&=2 \sqrt {2 x +y+1} \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 56

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

\[ x -\sqrt {2 x +y+1}-\frac {\ln \left (-1+\sqrt {2 x +y+1}\right )}{2}+\frac {\ln \left (\sqrt {2 x +y+1}+1\right )}{2}+\frac {\ln \left (2 x +y\right )}{2}-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 9.064 (sec). Leaf size: 48

DSolve[D[y[x],x]==2*Sqrt[2*x+y[x]+1],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to W\left (-e^{-x-\frac {3}{2}+c_1}\right ){}^2+2 W\left (-e^{-x-\frac {3}{2}+c_1}\right )-2 x \\ y(x)\to -2 x \\ \end{align*}