60.8.10 problem 1846

Internal problem ID [11771]
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 : Sunday, March 30, 2025 at 09:14:40 PM
CAS classification : [[_3rd_order, _missing_x]]

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

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

ode:=2*diff(y(x),x)*diff(diff(diff(y(x),x),x),x)-3*diff(y(x),x)^2 = 0; 
dsolve(ode,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*}

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

ode=-3*D[y[x],x]^2 + 2*D[y[x],x]*Derivative[3][y][x] == 0; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.207 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*Derivative(y(x), x)**2 + 2*Derivative(y(x), x)*Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} e^{- \frac {\sqrt {6} x}{2}} + C_{3} e^{\frac {\sqrt {6} x}{2}} \]