Internal problem ID [6074]
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]]
Solve \begin {gather*} \boxed {2 a y^{\prime \prime }+\left (y^{\prime }\right )^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.156 (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 \relax (x ) = 2 \sqrt {\left (x +c_{1}\right ) a}+c_{2} \\ y \relax (x ) = -2 \sqrt {\left (x +c_{1}\right ) a}+c_{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.442 (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*}