75.19.8 problem 625

Internal problem ID [17045]
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 15.4 Nonhomogeneous linear equations with constant coefficients. The Euler equations. Exercises page 143
Problem number : 625
Date solved : Thursday, March 13, 2025 at 09:11:43 AM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 15

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

\[ y = c_{1} +\ln \left (x \right ) c_{2} +c_{3} x^{3} \]

✓ Mathematica. Time used: 0.041 (sec). Leaf size: 24

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

\[ y(x)\to \frac {c_2 x^3}{3}+c_1 \log (x)+c_1+c_3 \]

✓ Sympy. Time used: 0.147 (sec). Leaf size: 14

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

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