Internal problem ID [7376]
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]
\[ \boxed {y^{\prime }-\sqrt {1+6 x +y}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 57
dsolve(diff(y(x),x)=(1+6*x+y(x))^(1/2),y(x), singsol=all)
\[ x -2 \sqrt {1+6 x +y \left (x \right )}+6 \ln \left (6+\sqrt {1+6 x +y \left (x \right )}\right )-6 \ln \left (-6+\sqrt {1+6 x +y \left (x \right )}\right )+6 \ln \left (-35+y \left (x \right )+6 x \right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 13.35 (sec). Leaf size: 65
DSolve[y'[x]==(1+6*x+y[x])^(1/2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 36 W\left (-\frac {1}{6} e^{\frac {1}{72} (-6 x-73+6 c_1)}\right ){}^2+72 W\left (-\frac {1}{6} e^{\frac {1}{72} (-6 x-73+6 c_1)}\right )-6 x+35 \\ y(x)\to 35-6 x \\ \end{align*}