Internal problem ID [6541]
Book: Own collection of miscellaneous problems
Section: section 5.0
Problem number: 1.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-A y^{\frac {2}{3}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.141 (sec). Leaf size: 61
dsolve(diff(y(x),x$2)=A*y(x)^(2/3),y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ \int _{}^{y \relax (x )}-\frac {5}{\sqrt {30 \textit {\_a}^{\frac {5}{3}} A -5 c_{1}}}d \textit {\_a} -x -c_{2} = 0 \\ \int _{}^{y \relax (x )}\frac {5}{\sqrt {30 \textit {\_a}^{\frac {5}{3}} A -5 c_{1}}}d \textit {\_a} -x -c_{2} = 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.088 (sec). Leaf size: 75
DSolve[y''[x]==A*y[x]^(2/3),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {y(x)^2 \left (1+\frac {6 A y(x)^{5/3}}{5 c_1}\right ) \, _2F_1\left (\frac {1}{2},\frac {3}{5};\frac {8}{5};-\frac {6 A y(x)^{5/3}}{5 c_1}\right ){}^2}{\frac {6}{5} A y(x)^{5/3}+c_1}=(x+c_2){}^2,y(x)\right ] \]