Internal problem ID [15437]
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: 672.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+\frac {2 y^{\prime }}{x}-y=4 \,{\mathrm e}^{x}} \] With initial conditions \begin {align*} [y \left (-\infty \right ) = 0, y^{\prime }\left (-1\right ) = -{\mathrm e}^{-1}] \end {align*}
✓ Solution by Maple
Time used: 0.141 (sec). Leaf size: 13
dsolve([diff(y(x),x$2)+2/x*diff(y(x),x)-y(x)=4*exp(x),y(-infinity) = 0, D(y)(-1) = -1/exp(1)],y(x), singsol=all)
\[ y \left (x \right ) = \left (x -1\right ) {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.079 (sec). Leaf size: 12
DSolve[{y''[x]+2/x*y'[x]-y[x]==4*Exp[x],{y[-Infinity]==0,y'[-1]==-1/Exp[1]}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^x (x-1) \]