Internal problem ID [5112]
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 3.5 HIGHER ORDER ODE. Page
181
Problem number: Example 3.38.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
Solve \begin {gather*} \boxed {x x^{\prime \prime }-\left (x^{\prime }\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.141 (sec). Leaf size: 14
dsolve(x(t)*diff(x(t),t$2)-diff(x(t),t)^2=0,x(t), singsol=all)
\begin{align*} x \relax (t ) = 0 \\ x \relax (t ) = {\mathrm e}^{c_{1} t} c_{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.034 (sec). Leaf size: 14
DSolve[x[t]*x''[t]-(x'[t])^2==0,x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_2 e^{c_1 t} \\ \end{align*}