7.7.30 problem 30

Internal problem ID [208]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Review problems at page 98
Problem number : 30
Date solved : Monday, January 27, 2025 at 02:41:37 AM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 42

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

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

✓ Solution by Mathematica

Time used: 7.936 (sec). Leaf size: 59

DSolve[D[y[x],x]==Sqrt[x+y[x]],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+1 \\ y(x)\to 1-x \\ \end{align*}