Internal problem ID [15386]
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 15.3 Nonhomogeneous linear equations with
constant coefficients. Initial value problem. Exercises page 140
Problem number: 617.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+4 y={\mathrm e}^{-x} \left (9 x^{2}+5 x -12\right )} \] With initial conditions \begin {align*} [y \left (\infty \right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.046 (sec). Leaf size: 14
dsolve([diff(y(x),x$2)-4*diff(y(x),x)+4*y(x)=exp(-x)*(9*x^2+5*x-12),y(infinity) = 0],y(x), singsol=all)
\[ y \left (x \right ) = -\operatorname {signum}\left (c_{1} {\mathrm e}^{2 x}\right ) \infty \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{y''[x]-4*y'[x]+4*y[x]==Exp[-x]*(9*x^2+5*x-12),{y[Infinity]==0}},y[x],x,IncludeSingularSolutions -> True]
{}