Internal problem ID [13426]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _dAlembert]
\[ \boxed {y^{\prime }-\sqrt {y+x}=0} \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 42
dsolve(diff(y(x),x)=sqrt(x+y(x)),y(x), singsol=all)
\[ x -2 \sqrt {x +y \left (x \right )}-\ln \left (\sqrt {x +y \left (x \right )}-1\right )+\ln \left (1+\sqrt {x +y \left (x \right )}\right )+\ln \left (x +y \left (x \right )-1\right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 8.647 (sec). Leaf size: 59
DSolve[y'[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*}