28.1.101 problem 124

Internal problem ID [4407]
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 : 124
Date solved : Monday, January 27, 2025 at 09:15:00 AM
CAS classification : [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

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

✓ Solution by Maple

Time used: 0.050 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.120 (sec). Leaf size: 16

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

\[ y(x)\to c_2 e^{c_1 e^x} \]