74.15.64 problem 64 (d)

Internal problem ID [16503]
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 (d)
Date solved : Tuesday, January 28, 2025 at 09:09:52 AM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+8 x^{3} y^{\prime \prime \prime }+27 x^{2} y^{\prime \prime }+35 x y^{\prime }+45 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 39

dsolve(x^4*diff(y(x),x$4)+8*x^3*diff(y(x),x$3)+27*x^2*diff(y(x),x$2)+35*x*diff(y(x),x)+45*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 44

DSolve[x^4*D[y[x],{x,4}]+8*x^3*D[y[x],{x,3}]+27*x^2*D[y[x],{x,2}]+35*x*D[y[x],x]+45*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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