Internal problem ID [4652]
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]]
\[ \boxed {y^{3} y^{\prime \prime }=k} \]
✓ Solution by Maple
Time used: 0.141 (sec). Leaf size: 70
dsolve(y(x)^3*diff(y(x),x$2)=k,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \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 \left (x \right ) = -\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: 2.878 (sec). Leaf size: 63
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}} y(x)\to \text {Indeterminate} \end{align*}