28.1.126 problem 149

Internal problem ID [4432]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 149
Date solved : Monday, January 27, 2025 at 09:17:13 AM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _with_potential_symmetries], [_2nd_order, _reducible, _mu_xy]]

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

✓ Solution by Maple

Time used: 0.055 (sec). Leaf size: 27

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

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

✓ Solution by Mathematica

Time used: 1.469 (sec). Leaf size: 43

DSolve[y[x]*D[y[x],{x,2}]-y[x]^2*D[y[x],x]-D[y[x],x]^2==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*}