Internal problem ID [12173]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 121.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]
\[ \boxed {y^{\prime \prime }-\frac {a}{y^{3}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 70
dsolve(diff(y(x),x$2)=a/y(x)^3,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}+a \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}+a \right )}}{c_{1}} \end{align*}
✓ Solution by Mathematica
Time used: 4.493 (sec). Leaf size: 63
DSolve[y''[x]==a/y[x]^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {a+c_1{}^2 (x+c_2){}^2}}{\sqrt {c_1}} y(x)\to \frac {\sqrt {a+c_1{}^2 (x+c_2){}^2}}{\sqrt {c_1}} y(x)\to \text {Indeterminate} \end{align*}