Internal problem ID [5264]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 3. Linear equations with variable coefficients. Page 124
Problem number: 2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }-x y^{\prime }+y=0} \end {gather*} Given that one solution of the ode is \begin {align*} y_1 &= x \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 13
dsolve([x^2*diff(y(x),x$2)-x*diff(y(x),x)+y(x)=0,x],y(x), singsol=all)
\[ y \relax (x ) = c_{1} x +c_{2} \ln \relax (x ) x \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 15
DSolve[x^2*y''[x]-x*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x (c_2 \log (x)+c_1) \\ \end{align*}