Internal problem ID [211]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.3, second order linear equations. Page 323
Problem number: 53.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+7 y^{\prime } x +25 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 25
dsolve(x^2*diff(y(x),x$2)+7*x*diff(y(x),x)+25*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \sin \left (4 \ln \relax (x )\right )}{x^{3}}+\frac {c_{2} \cos \left (4 \ln \relax (x )\right )}{x^{3}} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 26
DSolve[x^2*y''[x]+7*x*y'[x]+25*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_2 \cos (4 \log (x))+c_1 \sin (4 \log (x))}{x^3} \\ \end{align*}