7.5.16 problem 16

Internal problem ID [120]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.6 (substitution and exact equations). Problems at page 72
Problem number : 16
Date solved : Friday, February 07, 2025 at 07:52:52 AM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 44

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

\[ x -2 \sqrt {x +y+1}-\ln \left (-1+\sqrt {x +y+1}\right )+\ln \left (\sqrt {x +y+1}+1\right )+\ln \left (x +y\right )-c_1 = 0 \]

✓ Solution by Mathematica

Time used: 8.951 (sec). Leaf size: 56

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

\begin{align*} y(x)\to W\left (-e^{-\frac {x}{2}-1-\frac {c_1}{2}}\right ){}^2+2 W\left (-e^{-\frac {x}{2}-1-\frac {c_1}{2}}\right )-x \\ y(x)\to -x \\ \end{align*}