Internal problem ID [2276]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 35, page 157
Problem number: 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]
\[ \boxed {y^{3} y^{\prime \prime }=-4} \]
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 52
dsolve(y(x)^3*diff(y(x),x$2)+4=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {\sqrt {\left (2+c_{1} \left (c_{2} +x \right )\right ) \left (-2+c_{1} \left (c_{2} +x \right )\right ) c_{1}}}{c_{1}} \\ y \left (x \right ) &= -\frac {\sqrt {\left (2+c_{1} \left (c_{2} +x \right )\right ) \left (-2+c_{1} \left (c_{2} +x \right )\right ) c_{1}}}{c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 3.404 (sec). Leaf size: 93
DSolve[y[x]^3*y''[x]+4==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {c_1{}^2 x^2+2 c_2 c_1{}^2 x-4+c_2{}^2 c_1{}^2}}{\sqrt {c_1}} \\ y(x)\to \frac {\sqrt {c_1{}^2 x^2+2 c_2 c_1{}^2 x-4+c_2{}^2 c_1{}^2}}{\sqrt {c_1}} \\ y(x)\to \text {Indeterminate} \\ \end{align*}