44.1.57 problem 72

Internal problem ID [6932]
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 : 72
Date solved : Monday, January 27, 2025 at 02:37:14 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+20 x y^{\prime }-78 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 28

dsolve(x^3*diff(y(x),x$3)+2*x^2*diff(y(x),x$2)+20*x*diff(y(x),x)-78*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{1} x^{4}+c_{2} \sin \left (5 \ln \left (x \right )\right )+c_3 \cos \left (5 \ln \left (x \right )\right )}{x} \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 32

DSolve[x^3*D[y[x],{x,3}]+2*x^2*D[y[x],{x,2}]+20*x*D[y[x],x]-78*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_3 x^4+c_2 \cos (5 \log (x))+c_1 \sin (5 \log (x))}{x} \]