Internal problem ID [15315]
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: 545.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }+y=x^{2} {\mathrm e}^{-x} \cos \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(diff(y(x),x$2)+2*diff(y(x),x)+y(x)=x^2*exp(-x)*cos(x),y(x), singsol=all)
\[ y \left (x \right ) = -\left (\left (x^{2}-6\right ) \cos \left (x \right )-c_{1} x -4 \sin \left (x \right ) x -c_{2} \right ) {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.035 (sec). Leaf size: 32
DSolve[y''[x]+2*y'[x]+y[x]==x^2*Exp[-x]*Cos[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x} \left (-\left (x^2-6\right ) \cos (x)+4 x \sin (x)+c_2 x+c_1\right ) \]