75.14.24 problem 350

Internal problem ID [16867]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 14. Differential equations admitting of depression of their order. Exercises page 107
Problem number : 350
Date solved : Monday, March 31, 2025 at 03:33:48 PM
CAS classification : [[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]

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

✓ Maple. Time used: 0.040 (sec). Leaf size: 22

ode:=diff(diff(diff(y(x),x),x),x)+diff(diff(y(x),x),x)^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \ln \left (c_1 +x \right ) \left (c_1 +x \right )+\left (c_2 -1\right ) x -c_1 +c_3 \]

✓ Mathematica. Time used: 0.333 (sec). Leaf size: 28

ode=D[y[x],{x,3}]+D[y[x],{x,2}]^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to (-1+c_3) x+(x-c_1) \log (x-c_1)+c_2 \]

✓ Sympy. Time used: 0.275 (sec). Leaf size: 19

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

\[ y{\left (x \right )} = C_{1} + C_{3} \log {\left (C_{3} + x \right )} + x \left (C_{2} + \log {\left (C_{3} + x \right )}\right ) \]