Internal problem ID [6827]
Book: Elementary differential equations. By Earl D. Rainville, Phillip E. Bedient. Macmilliam
Publishing Co. NY. 6th edition. 1981.
Section: CHAPTER 16. Nonlinear equations. Section 101. Independent variable missing.
EXERCISES Page 324
Problem number: 7.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_y_y1]]
\[ \boxed {2 a y^{\prime \prime }+{y^{\prime }}^{3}=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 29
dsolve(2*a*diff(y(x),x$2)+diff(y(x),x)^3=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = 2 \sqrt {\left (x +c_{1} \right ) a}+c_{2} y \left (x \right ) = -2 \sqrt {\left (x +c_{1} \right ) a}+c_{2} \end{align*}
✓ Solution by Mathematica
Time used: 0.33 (sec). Leaf size: 51
DSolve[2*a*y''[x]+(y'[x])^3==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2-2 \sqrt {a} \sqrt {x-2 a c_1} y(x)\to 2 \sqrt {a} \sqrt {x-2 a c_1}+c_2 \end{align*}