75.18.28 problem 617

Internal problem ID [17116]
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 ODEs). Section 15.3 Nonhomogeneous linear equations with constant coefficients. Initial value problem. Exercises page 140
Problem number : 617
Date solved : Tuesday, January 28, 2025 at 09:53:26 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{-x} \left (9 x^{2}+5 x -12\right ) \end{align*}

With initial conditions

\begin{align*} y \left (\infty \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.301 (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)
 

\[ y = -\operatorname {signum}\left ({\mathrm e}^{2 x} c_{1} \right ) \infty \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[{D[y[x],{x,2}]-4*D[y[x],x]+4*y[x]==Exp[-x]*(9*x^2+5*x-12),{y[Infinity]==0}},y[x],x,IncludeSingularSolutions -> True]
 

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