Internal problem ID [6438]
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]
\[ \boxed {w^{\prime }+\frac {1}{2}+\frac {\sqrt {1-12 w}}{2}=0} \] With initial conditions \begin {align*} [w \left (1\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.687 (sec). Leaf size: 66
dsolve([diff(w(z),z) = -1/2 - sqrt(1/4 - 3*w(z)),w(1) = -1],w(z), singsol=all)
\[ w \left (z \right ) = \operatorname {RootOf}\left (-i \pi -\ln \left (1+\sqrt {13}\right )+\ln \left (-1+\sqrt {13}\right )+2 \sqrt {13}-2 \sqrt {1-12 \textit {\_Z}}+\ln \left (\textit {\_Z} \right )-\ln \left (-1+\sqrt {1-12 \textit {\_Z}}\right )+\ln \left (1+\sqrt {1-12 \textit {\_Z}}\right )+6 z -6\right ) \]
✓ Solution by Mathematica
Time used: 12.334 (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} W\left (\left (\sqrt {13}-1\right ) e^{-3 z+\sqrt {13}+2}\right ) \left (W\left (\left (\sqrt {13}-1\right ) e^{-3 z+\sqrt {13}+2}\right )+2\right ) \\ w(z)\to -\frac {1}{12} W\left (\left (\sqrt {13}-1\right ) e^{-3 z+\sqrt {13}+2}\right ) \left (W\left (\left (\sqrt {13}-1\right ) e^{-3 z+\sqrt {13}+2}\right )+2\right ) \\ \end{align*}