Internal problem ID [6439]
Book: Own collection of miscellaneous problems
Section: section 3.0
Problem number: 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {w^{\prime }+\frac {1}{2}+\frac {\sqrt {1-12 w}}{2}=0} \end {gather*} With initial conditions \begin {align*} [w \relax (1) = -1] \end {align*}
✓ Solution by Maple
Time used: 1.16 (sec). Leaf size: 66
dsolve([diff(w(z),z) = -1/2 - sqrt(1/4 - 3*w(z)),w(1) = -1],w(z), singsol=all)
\[ w \relax (z ) = \RootOf \left (-i \pi -2 \sqrt {1-12 \textit {\_Z}}+\ln \left (\textit {\_Z} \right )-\ln \left (-1+\sqrt {1-12 \textit {\_Z}}\right )+\ln \left (1+\sqrt {1-12 \textit {\_Z}}\right )-\ln \left (1+\sqrt {13}\right )+2 \sqrt {13}+\ln \left (-1+\sqrt {13}\right )+6 z -6\right ) \]
✓ Solution by Mathematica
Time used: 0.111 (sec). Leaf size: 105
DSolve[{w'[z] == -1/2 - Sqrt[1/4 - 3*w[z]],{w[1] == -1}},w[z],z,IncludeSingularSolutions -> True]
\begin{align*} w(z)\to -\frac {1}{12} \text {ProductLog}\left (\left (\sqrt {13}-1\right ) e^{-3 z+\sqrt {13}+2}\right ) \left (\text {ProductLog}\left (\left (\sqrt {13}-1\right ) e^{-3 z+\sqrt {13}+2}\right )+2\right ) \\ w(z)\to -\frac {1}{12} \text {ProductLog}\left (\left (\sqrt {13}-1\right ) e^{-3 z+\sqrt {13}+2}\right ) \left (\text {ProductLog}\left (\left (\sqrt {13}-1\right ) e^{-3 z+\sqrt {13}+2}\right )+2\right ) \\ \end{align*}