78.12.26 problem 5 (b)

Internal problem ID [18313]
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 (b)
Date solved : Tuesday, January 28, 2025 at 11:46:04 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} 2 x^{2} y^{\prime \prime }+10 x y^{\prime }+8 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 14

dsolve(2*x^2*diff(y(x),x$2)+10*x*diff(y(x),x)+8*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{2} \ln \left (x \right )+c_{1}}{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 18

DSolve[2*x^2*D[y[x],{x,2}] +10*x*D[y[x],x]+8*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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