Internal problem ID [15301]
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: 531.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }+5 y={\mathrm e}^{-x} \sin \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 28
dsolve(diff(y(x),x$2)+2*diff(y(x),x)+5*y(x)=exp(-x)*sin(2*x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {{\mathrm e}^{-x} \left (\left (x -4 c_{1} \right ) \cos \left (2 x \right )-4 \sin \left (2 x \right ) c_{2} \right )}{4} \]
✓ Solution by Mathematica
Time used: 0.083 (sec). Leaf size: 38
DSolve[y''[x]+2*y'[x]+5*y[x]==Exp[-x]*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{16} e^{-x} ((1+16 c_1) \sin (2 x)-4 (x-4 c_2) \cos (2 x)) \]