78.8.11 problem 11

Internal problem ID [18209]
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 : 11
Date solved : Tuesday, January 28, 2025 at 11:39:02 AM
CAS classification : [[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]

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

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 13

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

\[ y = -c_{1} \operatorname {arctanh}\left (c_{1} x \right )+c_{2} \]

✓ Solution by Mathematica

Time used: 0.853 (sec). Leaf size: 36

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

\begin{align*} y(x)\to c_2-\frac {\text {arctanh}\left (\frac {x}{\sqrt {c_1}}\right )}{\sqrt {c_1}} \\ y(x)\to \text {Indeterminate} \\ y(x)\to c_2 \\ \end{align*}