76.13.47 problem 56

Internal problem ID [17629]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.3 (Linear homogeneous equations with constant coefficients). Problems at page 239
Problem number : 56
Date solved : Tuesday, January 28, 2025 at 10:46:04 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }+3 x y^{\prime }+\frac {5 y}{4}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 23

dsolve(x^2*diff(y(x),x$2)+3*x*diff(y(x),x)+125/100*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 30

DSolve[x^2*D[y[x],{x,2}]+3*x*D[y[x],x]+125/100*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_2 \cos \left (\frac {\log (x)}{2}\right )+c_1 \sin \left (\frac {\log (x)}{2}\right )}{x} \]