76.13.51 problem 60

Internal problem ID [17633]
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 : 60
Date solved : Tuesday, January 28, 2025 at 10:46:10 AM
CAS classification : [[_Emden, _Fowler]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 29

dsolve(x^2*diff(y(x),x$2)+2*x*diff(y(x),x)+4*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{1} \sin \left (\frac {\sqrt {15}\, \ln \left (x \right )}{2}\right )+c_{2} \cos \left (\frac {\sqrt {15}\, \ln \left (x \right )}{2}\right )}{\sqrt {x}} \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 42

DSolve[x^2*D[y[x],{x,2}]+2*x*D[y[x],x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_2 \cos \left (\frac {1}{2} \sqrt {15} \log (x)\right )+c_1 \sin \left (\frac {1}{2} \sqrt {15} \log (x)\right )}{\sqrt {x}} \]