Internal problem ID [12395]
Book: Differential Equations, Linear, Nonlinear, Ordinary, Partial. A.C. King, J.Billingham,
S.R.Otto. Cambridge Univ. Press 2003
Section: Chapter 1 VARIABLE COEFFICIENT, SECOND ORDER DIFFERENTIAL
EQUATIONS. Problems page 28
Problem number: Problem 1.1(b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Lienard]
\[ \boxed {x y^{\prime \prime }+2 y^{\prime }+y x=0} \] Given that one solution of the ode is \begin {align*} y_1 &= \frac {\sin \left (x \right )}{x} \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve([x*diff(y(x),x$2)+2*diff(y(x),x)+x*y(x)=0,sin(x)/x],singsol=all)
\[ y \left (x \right ) = \frac {c_{1} \sin \left (x \right )+c_{2} \cos \left (x \right )}{x} \]
✓ Solution by Mathematica
Time used: 0.046 (sec). Leaf size: 37
DSolve[x*y''[x]+2*y'[x]+x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {2 c_1 e^{-i x}-i c_2 e^{i x}}{2 x} \]