48.4.23 problem Problem 3.38

Internal problem ID [7565]
Book : THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T. CHAU, CRC Press. Boca Raton, FL. 2018
Section : Chapter 3. Ordinary Differential Equations. Section 3.6 Summary and Problems. Page 218
Problem number : Problem 3.38
Date solved : Monday, January 27, 2025 at 03:06:20 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _with_potential_symmetries], [_2nd_order, _reducible, _mu_xy]]

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

✓ Solution by Maple

Time used: 0.036 (sec). Leaf size: 27

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

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

✓ Solution by Mathematica

Time used: 1.838 (sec). Leaf size: 43

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

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