44.1.24 problem 26

Internal problem ID [6899]
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 : Monday, January 27, 2025 at 02:34:26 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*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 30

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

\[ y = \frac {4 c_{2} x^{2} \ln \left (x \right )+4 c_3 \,x^{2}+16 x^{3}+c_{1}}{4 x} \]

✓ Solution by Mathematica

Time used: 0.008 (sec). Leaf size: 27

DSolve[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,y[x],x,IncludeSingularSolutions -> True]
 

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