75.19.7 problem 624

Internal problem ID [17044]
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 : 624
Date solved : Thursday, March 13, 2025 at 09:11:42 AM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 16

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

\[ y = c_{3} x^{4}+c_{2} x^{2}+c_{1} \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 26

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

\[ y(x)\to \frac {c_2 x^4}{4}+\frac {c_1 x^2}{2}+c_3 \]

✓ Sympy. Time used: 0.152 (sec). Leaf size: 14

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

\[ y{\left (x \right )} = C_{1} + C_{2} x^{2} + C_{3} x^{4} \]