74.15.17 problem 17

Internal problem ID [16456]
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 : 17
Date solved : Tuesday, January 28, 2025 at 09:08:21 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 18

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

\[ y = x \left (c_{1} +c_{2} \sin \left (\ln \left (x \right )\right )+c_{3} \cos \left (\ln \left (x \right )\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 22

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

\[ y(x)\to x (c_2 \cos (\log (x))+c_1 \sin (\log (x))+c_3) \]