Internal problem ID [6623]
Book: First order enumerated odes
Section: section 1
Problem number: 60.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime }-\sqrt {1+6 x +y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.023 (sec). Leaf size: 57
dsolve(diff(y(x),x)=(1+6*x+y(x))^(1/2),y(x), singsol=all)
\[ x -2 \sqrt {1+6 x +y \relax (x )}-6 \ln \left (-6+\sqrt {1+6 x +y \relax (x )}\right )+6 \ln \left (6+\sqrt {1+6 x +y \relax (x )}\right )+6 \ln \left (-35+6 x +y \relax (x )\right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.134 (sec). Leaf size: 54
DSolve[y'[x]==(1+6*x+y[x])^(1/2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 36 \text {ProductLog}\left (-\frac {1}{6} e^{\frac {1}{72} (-6 x-73+6 c_1)}\right ) \left (2+\text {ProductLog}\left (-\frac {1}{6} e^{\frac {1}{72} (-6 x-73+6 c_1)}\right )\right )-6 x+35 \\ \end{align*}