78.8.7 problem 7

Internal problem ID [18205]
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 : 7
Date solved : Tuesday, January 28, 2025 at 11:38:18 AM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

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

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 37

dsolve(y(x)*diff(y(x),x$2)+diff(y(x),x)^2-2*y(x)*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.725 (sec). Leaf size: 38

DSolve[y[x]*D[y[x],{x,2}]+D[y[x],x]^2-2*y[x]*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_2 \sqrt {e^{2 x}+e^{c_1}} \\ y(x)\to c_2 \sqrt {e^{2 x}} \\ \end{align*}