Internal problem ID [15352]
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: 583.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }=-1+3 \sin \left (2 x \right )+\cos \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 36
dsolve(diff(y(x),x$2)+2*diff(y(x),x)+1=3*sin(2*x)+cos(x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {{\mathrm e}^{-2 x} c_{1}}{2}+\frac {2 \sin \left (x \right )}{5}-\frac {3 \sin \left (2 x \right )}{8}-\frac {\cos \left (x \right )}{5}-\frac {3 \cos \left (2 x \right )}{8}-\frac {x}{2}+c_{2} \]
✓ Solution by Mathematica
Time used: 0.316 (sec). Leaf size: 52
DSolve[y''[x]+2*y'[x]+1==3*Sin[2*x]+Cos[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {x}{2}+\frac {2 \sin (x)}{5}-\frac {3}{8} \sin (2 x)-\frac {\cos (x)}{5}-\frac {3}{8} \cos (2 x)-\frac {1}{2} c_1 e^{-2 x}+c_2 \]