82.35.1 problem Ex. 1

Internal problem ID [18925]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VII. Linear equations with variable coefficients. Problems at page 85
Problem number : Ex. 1
Date solved : Tuesday, January 28, 2025 at 12:37:12 PM
CAS classification : [[_3rd_order, _exact, _linear, _homogeneous]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 36

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

\[ y \left (x \right ) = \frac {x^{{3}/{2}} \sin \left (\frac {\sqrt {3}\, \ln \left (x \right )}{2}\right ) c_{2} +c_3 \,x^{{3}/{2}} \cos \left (\frac {\sqrt {3}\, \ln \left (x \right )}{2}\right )+c_{1}}{x} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 52

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

\[ y(x)\to \frac {c_3 x^{3/2} \cos \left (\frac {1}{2} \sqrt {3} \log (x)\right )+c_2 x^{3/2} \sin \left (\frac {1}{2} \sqrt {3} \log (x)\right )+c_1}{x} \]