8.5.16 problem 16

Internal problem ID [744]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.6, Substitution methods and exact equations. Page 74
Problem number : 16
Date solved : Monday, January 27, 2025 at 03:02:15 AM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 44

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

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

✓ Solution by Mathematica

Time used: 8.116 (sec). Leaf size: 56

DSolve[D[y[x],x] == (1+x+y[x])^(1/2),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*}