Internal problem ID [15349]
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. Superposition principle. Exercises page 137
Problem number: 580.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }+y=1+2 \cos \left (x \right )+\cos \left (2 x \right )-\sin \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 30
dsolve(diff(y(x),x$2)+2*diff(y(x),x)+y(x)=1+2*cos(x)+cos(2*x)-sin(2*x),y(x), singsol=all)
\[ y \left (x \right ) = 1+\left (c_{1} x +c_{2} \right ) {\mathrm e}^{-x}+\sin \left (x \right )+\frac {\cos \left (2 x \right )}{25}+\frac {7 \sin \left (2 x \right )}{25} \]
✓ Solution by Mathematica
Time used: 1.184 (sec). Leaf size: 42
DSolve[y''[x]+2*y'[x]+y[x]==1+2*Cos[x]+Cos[2*x]-Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \sin (x)+\frac {7}{25} \sin (2 x)+\frac {1}{25} \cos (2 x)+c_1 e^{-x}+c_2 e^{-x} x+1 \]