Internal problem ID [15257]
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. Trial and error method. Exercises page 132
Problem number: 487.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+6 y^{\prime }+13 y={\mathrm e}^{-3 x} \cos \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 30
dsolve(diff(y(x),x$2)+6*diff(y(x),x)+13*y(x)=exp(-3*x)*cos(2*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{-3 x} \left (\sin \left (2 x \right ) \left (x +4 c_{2} \right )+4 \cos \left (2 x \right ) \left (c_{1} +\frac {1}{8}\right )\right )}{4} \]
✓ Solution by Mathematica
Time used: 0.094 (sec). Leaf size: 38
DSolve[y''[x]+6*y'[x]+13*y[x]==Exp[-3*x]*Cos[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{16} e^{-3 x} ((1+16 c_2) \cos (2 x)+4 (x+4 c_1) \sin (2 x)) \]