Internal problem ID [2301]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 8, Linear differential equations of order n. Section 8.8, A Differential Equation with
Nonconstant Coefficients. page 567
Problem number: Problem 22.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {x^{2} y^{\prime \prime }-y^{\prime } x +5 y=0} \] With initial conditions \begin {align*} \left [y \left (1\right ) = \sqrt {2}, y^{\prime }\left (1\right ) = 3 \sqrt {2}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 20
dsolve([x^2*diff(y(x),x$2)-x*diff(y(x),x)+5*y(x)=0,y(1) = 2^(1/2), D(y)(1) = 3*2^(1/2)],y(x), singsol=all)
\[ y \left (x \right ) = \sqrt {2}\, x \left (\sin \left (2 \ln \left (x \right )\right )+\cos \left (2 \ln \left (x \right )\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 23
DSolve[{x^2*y''[x]-x*y'[x]+5*y[x]==0,{y[1]==Sqrt[2],y'[1]==3*Sqrt[2]}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt {2} x (\sin (2 \log (x))+\cos (2 \log (x))) \\ \end{align*}