78.15.23 problem 23

Internal problem ID [18379]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 22. Higher Order Linear Equations. Coupled Harmonic Oscillators. Problems at page 160
Problem number : 23
Date solved : Tuesday, January 28, 2025 at 11:48:31 AM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} x^{3} y^{\prime \prime \prime \prime }+8 x^{2} y^{\prime \prime \prime }+8 x y^{\prime \prime }-8 y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 21

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

\[ y = c_{1} +c_{2} x^{2}+\frac {c_3}{x^{3}}+\frac {c_4}{x} \]

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 33

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

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