78.8.41 problem 41

Internal problem ID [18239]
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 : 41
Date solved : Tuesday, January 28, 2025 at 11:43:21 AM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]

\begin{align*} y^{2} y^{\prime \prime }+{y^{\prime }}^{3}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 29

dsolve(y(x)^2* diff(y(x),x$2)+ (diff(y(x),x))^3 = 0,y(x), singsol=all)
 

\begin{align*} y &= 0 \\ y &= c_{1} \\ y &= -\frac {\operatorname {LambertW}\left (-c_{1} {\mathrm e}^{-c_{2} -x}\right )}{c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.660 (sec). Leaf size: 37

DSolve[y[x]^2 * D[y[x],{x,2}]+ D[y[x],x]^3 == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2 \left (1+\frac {1}{\text {InverseFunction}\left [-\frac {1}{\text {$\#$1}}-\log (\text {$\#$1})+\log (\text {$\#$1}+1)\&\right ][-x+c_1]}\right ) \]