78.8.1 problem 1

Internal problem ID [18199]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Miscellaneous Problems for Chapter 2. Problems at page 99
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 11:37:59 AM
CAS classification : [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} y y^{\prime \prime }&={y^{\prime }}^{2} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 14

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

\begin{align*} y &= 0 \\ y &= {\mathrm e}^{c_{1} x} c_{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.099 (sec). Leaf size: 14

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

\[ y(x)\to c_2 e^{c_1 x} \]