74.15.49 problem 52

Internal problem ID [16417]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.7, page 195
Problem number : 52
Date solved : Monday, March 31, 2025 at 02:52:47 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-3 x y^{\prime }&=-8 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 24

ode:=x^3*diff(diff(diff(y(x),x),x),x)+3*x^2*diff(diff(y(x),x),x)-3*x*diff(y(x),x) = -8; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1 \,x^{2}}{2}+2 \ln \left (x \right )-\frac {c_1 +c_2}{2 x^{2}}+c_3 \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 30

ode=x^3*D[y[x],{x,3}]+3*x^2*D[y[x],{x,2}]-3*x*D[y[x],x]==-8; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.266 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3*Derivative(y(x), (x, 3)) + 3*x**2*Derivative(y(x), (x, 2)) - 3*x*Derivative(y(x), x) + 8,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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