Internal problem ID [15385]
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: 616.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-5 y^{\prime }+6 y=2 \,{\mathrm e}^{-2 x} \left (9 \sin \left (2 x \right )+4 \cos \left (2 x \right )\right )} \] With initial conditions \begin {align*} [y \left (\infty \right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 31
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)
\[ y \left (x \right ) = c_{2} {\mathrm e}^{2 x}+\frac {\left (113 \cos \left (2 x \right )+36 \sin \left (2 x \right )\right ) {\mathrm e}^{-2 x}}{145} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{y''[x]-5*y'[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