53.4.7 problem 7

Internal problem ID [8495]
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
Date solved : Monday, January 27, 2025 at 04:07:23 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_y_y1]]

\begin{align*} 2 a y^{\prime \prime }+{y^{\prime }}^{3}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.026 (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 &= 2 \sqrt {\left (x +c_{1} \right ) a}+c_{2} \\ y &= -2 \sqrt {\left (x +c_{1} \right ) a}+c_{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.395 (sec). Leaf size: 51

DSolve[2*a*D[y[x],{x,2}]+(D[y[x],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*}