Internal problem ID [15433]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 15.5 Linear equations with variable coefficients.
The Lagrange method. Exercises page 148
Problem number: 668.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {4 x y^{\prime \prime }+2 y^{\prime }+y=\frac {6+x}{x^{2}}} \] With initial conditions \begin {align*} [y \left (\infty \right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.75 (sec). Leaf size: 41
dsolve([4*x*diff(y(x),x$2)+2*diff(y(x),x)+y(x)=(6+x)/x^2,y(infinity) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \textit {undefined} \]
✓ Solution by Mathematica
Time used: 0.192 (sec). Leaf size: 27
DSolve[{4*x*y''[x]+2*y'[x]+y[x]==(6+x)/x^2,{y[Infinity]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{x}+c_1 \cos \left (\sqrt {x}\right )+c_2 \sin \left (\sqrt {x}\right ) \]