78.15.20 problem 22 (a)

Internal problem ID [18376]
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 : 22 (a)
Date solved : Tuesday, January 28, 2025 at 11:48:30 AM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 21

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

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