53.4.6 problem 6

Internal problem ID [8494]
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 : 6
Date solved : Monday, January 27, 2025 at 04:07:22 PM
CAS classification : [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} \left (y+1\right ) y^{\prime \prime }&={y^{\prime }}^{2} \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 16

dsolve((y(x)+1)*diff(y(x),x$2)=diff(y(x),x)^2,y(x), singsol=all)
 

\begin{align*} y &= -1 \\ y &= {\mathrm e}^{c_{1} x} c_{2} -1 \\ \end{align*}

✓ Solution by Mathematica

Time used: 1.324 (sec). Leaf size: 26

DSolve[(y[x]+1)*D[y[x],{x,2}]==(D[y[x],x])^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -1+\frac {e^{c_1 (x+c_2)}}{c_1} \\ y(x)\to \text {Indeterminate} \\ \end{align*}