74.15.63 problem 64 (c)

Internal problem ID [16502]
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 : 64 (c)
Date solved : Tuesday, January 28, 2025 at 09:09:52 AM
CAS classification : [[_high_order, _exact, _linear, _homogeneous]]

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+14 x^{3} y^{\prime \prime \prime }+55 x^{2} y^{\prime \prime }+65 x y^{\prime }+15 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 27

dsolve(x^4*diff(y(x),x$4)+14*x^3*diff(y(x),x$3)+55*x^2*diff(y(x),x$2)+65*x*diff(y(x),x)+15*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{3} x \sin \left (\ln \left (x \right )\right )+c_4 \cos \left (\ln \left (x \right )\right ) x +c_{2} x^{2}+c_{1}}{x^{3}} \]

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 32

DSolve[x^4*D[y[x],{x,4}]+14*x^3*D[y[x],{x,3}]+55*x^2*D[y[x],{x,2}]+65*x*D[y[x],x]+15*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_4 x^2+c_2 x \cos (\log (x))+c_1 x \sin (\log (x))+c_3}{x^3} \]