73.7.4 problem 4

Internal problem ID [15162]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 8. Review exercises for part of part II. page 143
Problem number : 4
Date solved : Tuesday, January 28, 2025 at 07:38:53 AM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.066 (sec). Leaf size: 42

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

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

✓ Solution by Mathematica

Time used: 8.171 (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*}