78.9.12 problem 7

Internal problem ID [18260]
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 14. Introduction. Problems at page 112
Problem number : 7
Date solved : Tuesday, January 28, 2025 at 11:44:38 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }-5 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 15

dsolve(x^2*diff(y(x),x$2)-3*x*diff(y(x),x)-5*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{1} x^{6}+c_{2}}{x} \]

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 18

DSolve[x^2*D[y[x],{x,2}] -3*x*D[y[x],x]-5*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_2 x^6+c_1}{x} \]