Internal problem ID [5253]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 3. Linear equations with variable coefficients. Page 108
Problem number: 1(c.1).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 1, y^{\prime }\relax (1) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 13
dsolve([diff(y(x),x$2)+1/x*diff(y(x),x)-1/x^2*y(x)=0,y(1) = 1, D(y)(1) = 0],y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{2}+1}{2 x} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 17
DSolve[{y''[x]+1/x*y'[x]-1/x^2*y[x]==0,{y[1]==1,y'[1]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^2+1}{2 x} \\ \end{align*}