78.12.27 problem 5 (c)

Internal problem ID [18314]
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 17. The Homogeneous Equation with Constant Coefficients. Problems at page 125
Problem number : 5 (c)
Date solved : Tuesday, January 28, 2025 at 11:46:05 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }+2 x y^{\prime }-12 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 15

dsolve(x^2*diff(y(x),x$2)+2*x*diff(y(x),x)-12*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{1} x^{7}+c_{2}}{x^{4}} \]

✓ Solution by Mathematica

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

DSolve[x^2*D[y[x],{x,2}] +2*x*D[y[x],x]-12*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_2 x^7+c_1}{x^4} \]