63.1.82 problem 127

Internal problem ID [15522]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 127
Date solved : Thursday, October 02, 2025 at 10:19:31 AM
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} \end{align*}

✓ Maple. Time used: 0.037 (sec). Leaf size: 24

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

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

✓ Mathematica. Time used: 0.192 (sec). Leaf size: 24

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

\begin{align*} y(x)&\to x+c_3 x-(x+c_1) \log (x+c_1)+c_2 \end{align*}

✓ Sympy. Time used: 0.158 (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)
 

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