Internal problem ID [6090]
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: 25.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-{\mathrm e}^{x} \left (y^{\prime }\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 25
dsolve(diff(y(x),x$2)=exp(x)*diff(y(x),x)^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {\ln \left ({\mathrm e}^{x}\right )}{c_{1}}-\frac {\ln \left (-c_{1}+{\mathrm e}^{x}\right )}{c_{1}}+c_{2} \]
✓ Solution by Mathematica
Time used: 1.485 (sec). Leaf size: 37
DSolve[y''[x]==Exp[x](y'[x])^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {-x+\log \left (e^x+c_1\right )+c_1 c_2}{c_1} \\ y(x)\to \text {Indeterminate} \\ y(x)\to c_2 \\ \end{align*}