75.18.27 problem 616

Internal problem ID [17115]
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 : 616
Date solved : Tuesday, January 28, 2025 at 09:53:24 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=2 \,{\mathrm e}^{-2 x} \left (9 \sin \left (2 x \right )+4 \cos \left (2 x \right )\right ) \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.470 (sec). Leaf size: 14

dsolve([diff(y(x),x$2)-5*diff(y(x),x)+6*y(x)=2*exp(-2*x)*(9*sin(2*x)+4*cos(2*x)),y(infinity) = 0],y(x), singsol=all)
 

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

✗ Solution by Mathematica

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

DSolve[{D[y[x],{x,2}]-5*D[y[x],x]+6*y[x]==2*Exp[-2*x]*(9*Sin[2*x]+4*Cos[2*x]),{y[Infinity]==0}},y[x],x,IncludeSingularSolutions -> True]
 

Not solved