4.23 problem Problem 3.38

Internal problem ID [5144]

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.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _with_potential_symmetries], [_2nd_order, _reducible, _mu_xy]]

Solve \begin {gather*} \boxed {y y^{\prime \prime }-\left (y^{\prime }\right )^{2}-y^{2} y^{\prime }=0} \end {gather*}

Solution by Maple

Time used: 10.156 (sec). Leaf size: 32

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

Solution by Mathematica

Time used: 0.186 (sec). Leaf size: 25

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

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