Internal problem ID [3145]
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]
\[ \boxed {y^{2} y^{\prime }-3 y^{6}=2} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.235 (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 \left (x \right ) &= \frac {3^{\frac {5}{6}} 2^{\frac {1}{6}} \tan \left (3 \sqrt {6}\, x \right )^{\frac {1}{3}}}{3} \\ y \left (x \right ) &= \frac {\tan \left (3 \sqrt {6}\, x \right )^{\frac {1}{3}} \left (3 i 3^{\frac {1}{6}}-3^{\frac {2}{3}}\right ) 6^{\frac {1}{6}}}{6} \\ y \left (x \right ) &= -\frac {\tan \left (3 \sqrt {6}\, x \right )^{\frac {1}{3}} \left (3 i 3^{\frac {1}{6}}+3^{\frac {2}{3}}\right ) 6^{\frac {1}{6}}}{6} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.017 (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*}