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]
\[ \boxed {y^{\prime }-\sqrt {x +y}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 42
dsolve(diff(y(x),x)=(x+y(x))^(1/2),y(x), singsol=all)
\[ x -2 \sqrt {x +y \left (x \right )}-\ln \left (-1+\sqrt {x +y \left (x \right )}\right )+\ln \left (1+\sqrt {x +y \left (x \right )}\right )+\ln \left (x +y \left (x \right )-1\right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 9.242 (sec). Leaf size: 59
DSolve[y'[x]==(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+1 y(x)\to 1-x \end{align*}