Internal problem ID [969]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Existence and Uniqueness of Solutions of Nonlinear
Equations. Section 2.3 Page 60
Problem number: 12.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime }-\sqrt {x +y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 42
dsolve(diff(y(x),x)=(x+y(x))^(1/2),y(x), singsol=all)
\[ x -2 \sqrt {x +y \relax (x )}-\ln \left (-1+\sqrt {x +y \relax (x )}\right )+\ln \left (1+\sqrt {x +y \relax (x )}\right )+\ln \left (x +y \relax (x )-1\right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.079 (sec). Leaf size: 49
DSolve[y'[x]==(x+y[x])^(1/2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {ProductLog}\left (-e^{-\frac {x}{2}-1-\frac {c_1}{2}}\right ) \left (2+\text {ProductLog}\left (-e^{-\frac {x}{2}-1-\frac {c_1}{2}}\right )\right )-x+1 \\ \end{align*}