Internal problem ID [4144]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 8. Special second order equations. Lesson 35. Independent variable x
absent
Problem number: Exercise 35.2, page 504.
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^{3} y^{\prime \prime }-k=0} \end {gather*}
✓ Solution by Maple
Time used: 0.104 (sec). Leaf size: 70
dsolve(y(x)^3*diff(y(x),x$2)=k,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\sqrt {c_{1} \left (c_{1}^{2} c_{2}^{2}+2 c_{1}^{2} c_{2} x +c_{1}^{2} x^{2}+k \right )}}{c_{1}} \\ y \relax (x ) = -\frac {\sqrt {c_{1} \left (c_{1}^{2} c_{2}^{2}+2 c_{1}^{2} c_{2} x +c_{1}^{2} x^{2}+k \right )}}{c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.97 (sec). Leaf size: 58
DSolve[y[x]^3*y''[x]==k,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {k+c_1{}^2 (x+c_2){}^2}}{\sqrt {c_1}} \\ y(x)\to \frac {\sqrt {k+c_1{}^2 (x+c_2){}^2}}{\sqrt {c_1}} \\ \end{align*}