44.1.38 problem 40

Internal problem ID [6913]
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 : 40
Date solved : Monday, January 27, 2025 at 02:34:50 PM
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*}

✓ Solution by Maple

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

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

\[ y = c_3 \,x^{4}+c_{2} x^{2}+c_{1} \]

✓ Solution by Mathematica

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

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

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