Internal problem ID [94]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.6, Substitution methods and exact equations. Page 74
Problem number: 16.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime }-\sqrt {1+x +y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 44
dsolve(diff(y(x),x) = (1+x+y(x))^(1/2),y(x), singsol=all)
\[ x -2 \sqrt {1+x +y \relax (x )}-\ln \left (-1+\sqrt {1+x +y \relax (x )}\right )+\ln \left (1+\sqrt {1+x +y \relax (x )}\right )+\ln \left (x +y \relax (x )\right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.044 (sec). Leaf size: 48
DSolve[y'[x] == (1+x+y[x])^(1/2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x+\text {ProductLog}\left (-e^{\frac {1}{2} (-x-3-c_1)}\right ) \left (2+\text {ProductLog}\left (-e^{\frac {1}{2} (-x-3-c_1)}\right )\right ) \\ \end{align*}