78.8.46 problem 46

Internal problem ID [18244]
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 : 46
Date solved : Tuesday, January 28, 2025 at 11:44:08 AM
CAS classification : [[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]

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

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 21

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

\[ y = \frac {x}{c_{1}}+\frac {\ln \left (c_{1} x -1\right )}{c_{1}^{2}}+c_{2} \]

✓ Solution by Mathematica

Time used: 0.515 (sec). Leaf size: 47

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

\begin{align*} y(x)\to -\frac {x}{c_1}+\frac {\log (1+c_1 x)}{c_1{}^2}+c_2 \\ y(x)\to c_2 \\ y(x)\to -\frac {x^2}{2}+c_2 \\ \end{align*}