Internal problem ID [5897]
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]]
\[ \boxed {y y^{\prime \prime }-{y^{\prime }}^{2}-y^{\prime } y^{2}=0} \]
✓ Solution by Maple
Time used: 0.063 (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 \left (x \right ) &= 0 \\ y \left (x \right ) &= -\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: 1.53 (sec). Leaf size: 43
DSolve[y[x]*y''[x]-(y'[x])^2-y[x]^2*y'[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*}