50.13.22 problem 19(c)

Internal problem ID [8037]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Section 2.7. HIGHER ORDER LINEAR EQUATIONS, COUPLED HARMONIC OSCILLATORS Page 98
Problem number : 19(c)
Date solved : Monday, January 27, 2025 at 03:37:00 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 18

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

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

✓ Solution by Mathematica

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

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

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