15.18.4 problem 4

Internal problem ID [3247]
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
Date solved : Monday, January 27, 2025 at 07:27:30 AM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

\begin{align*} y^{3} y^{\prime \prime }+4&=0 \end{align*}

✓ Solution by Maple

Time used: 0.035 (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: 3.061 (sec). Leaf size: 93

DSolve[y[x]^3*D[y[x],{x,2}]+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*}