Internal problem ID [6007]
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.2).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
\[ \boxed {y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}}=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 0, y^{\prime }\left (1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 13
dsolve([diff(y(x),x$2)+1/x*diff(y(x),x)-1/x^2*y(x)=0,y(1) = 0, D(y)(1) = 1],y(x), singsol=all)
\[ y \left (x \right ) = -\frac {1}{2 x}+\frac {x}{2} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 17
DSolve[{y''[x]+1/x*y'[x]-1/x^2*y[x]==0,{y[1]==0,y'[1]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x^2-1}{2 x} \]