48.3.9 problem Example 3.38

Internal problem ID [7533]
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
Date solved : Monday, January 27, 2025 at 03:04:44 PM
CAS classification : [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

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

✓ Solution by Maple

Time used: 0.015 (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 \left (t \right ) &= 0 \\ x \left (t \right ) &= {\mathrm e}^{c_{1} t} c_{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.116 (sec). Leaf size: 14

DSolve[x[t]*D[x[t],{t,2}]-(D[x[t],t])^2==0,x[t],t,IncludeSingularSolutions -> True]
 

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