38.1.24 problem 26

Internal problem ID [8185]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Exercises 1.1 at page 12
Problem number : 26
Date solved : Tuesday, September 30, 2025 at 05:18:26 PM
CAS classification : [[_3rd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-x y^{\prime }+y&=12 x^{2} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 30

ode:=x^3*diff(diff(diff(y(x),x),x),x)+2*x^2*diff(diff(y(x),x),x)-x*diff(y(x),x)+y(x) = 12*x^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {4 x^{2} c_2 \ln \left (x \right )+4 c_3 \,x^{2}+16 x^{3}+c_1}{4 x} \]

✓ Mathematica. Time used: 0.006 (sec). Leaf size: 27

ode=x^3*D[y[x],{x,3}]+2*x^2*D[y[x],{x,2}]-x*D[y[x],x]+y[x]==12*x^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 4 x^2+c_2 x+\frac {c_1}{x}+c_3 x \log (x) \end{align*}

✓ 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)) + 2*x**2*Derivative(y(x), (x, 2)) - 12*x**2 - x*Derivative(y(x), x) + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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