Internal problem ID [2636]
Book: An introduction to the solution and applications of differential equations, J.W. Searl,
1966
Section: Chapter 4, Ex. 4.2
Problem number: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime } y^{2}-2-3 y^{6}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.099 (sec). Leaf size: 77
dsolve([y(x)^2*diff(y(x),x)=2+3*y(x)^6,y(0) = 0],y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {3^{\frac {5}{6}} 2^{\frac {1}{6}} \left (\tan ^{\frac {1}{3}}\left (3 \sqrt {6}\, x \right )\right )}{3} \\ y \relax (x ) = \frac {2^{\frac {1}{6}} \left (\tan ^{\frac {1}{3}}\left (3 \sqrt {6}\, x \right )\right ) \left (-3^{\frac {5}{6}}+3 i 3^{\frac {1}{3}}\right )}{6} \\ y \relax (x ) = -\frac {2^{\frac {1}{6}} \left (\tan ^{\frac {1}{3}}\left (3 \sqrt {6}\, x \right )\right ) \left (3^{\frac {5}{6}}+3 i 3^{\frac {1}{3}}\right )}{6} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 87
DSolve[{y[x]^2*y'[x]==2+3*y[x]^6,y[0]==0},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt [6]{\frac {2}{3}} \sqrt [3]{\tan \left (3 \sqrt {6} x\right )} \\ y(x)\to -\sqrt [3]{-1} \sqrt [6]{\frac {2}{3}} \sqrt [3]{\tan \left (3 \sqrt {6} x\right )} \\ y(x)\to (-1)^{2/3} \sqrt [6]{\frac {2}{3}} \sqrt [3]{\tan \left (3 \sqrt {6} x\right )} \\ \end{align*}