60.8.10 problem 1846

Internal problem ID [11845]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 7, non-linear third and higher order
Problem number : 1846
Date solved : Monday, January 27, 2025 at 11:43:32 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 2 y^{\prime } y^{\prime \prime \prime }-3 {y^{\prime }}^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 28

dsolve(2*diff(y(x),x)*diff(diff(diff(y(x),x),x),x)-3*diff(y(x),x)^2=0,y(x), singsol=all)
 

\begin{align*} y &= c_{1} +c_{2} {\mathrm e}^{\frac {\sqrt {6}\, x}{2}}+c_3 \,{\mathrm e}^{-\frac {\sqrt {6}\, x}{2}} \\ y &= c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.068 (sec). Leaf size: 57

DSolve[-3*D[y[x],x]^2 + 2*D[y[x],x]*Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 \\ y(x)\to \sqrt {\frac {2}{3}} e^{-\sqrt {\frac {3}{2}} x} \left (c_1 e^{\sqrt {6} x}-c_2\right )+c_3 \\ y(x)\to c_1 \\ \end{align*}