75.19.3 problem 620

Internal problem ID [17119]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 15.4 Nonhomogeneous linear equations with constant coefficients. The Euler equations. Exercises page 143
Problem number : 620
Date solved : Tuesday, January 28, 2025 at 09:53:31 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }+2 x y^{\prime }+6 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 29

dsolve(x^2*diff(y(x),x$2)+2*x*diff(y(x),x)+6*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{1} \sin \left (\frac {\sqrt {23}\, \ln \left (x \right )}{2}\right )+c_{2} \cos \left (\frac {\sqrt {23}\, \ln \left (x \right )}{2}\right )}{\sqrt {x}} \]

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 42

DSolve[x^2*D[y[x],{x,2}]+2*x*D[y[x],x]+6*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_2 \cos \left (\frac {1}{2} \sqrt {23} \log (x)\right )+c_1 \sin \left (\frac {1}{2} \sqrt {23} \log (x)\right )}{\sqrt {x}} \]