Internal problem ID [15254]
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: 484.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+16 y=\sin \left (4 x +\alpha \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
dsolve(diff(y(x),x$2)+16*y(x)=sin(4*x+alpha),y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (4 x \right ) c_{2} +\cos \left (4 x \right ) c_{1} -\frac {x \cos \left (4 x +\alpha \right )}{8}+\frac {\sin \left (4 x +\alpha \right )}{64} \]
✓ Solution by Mathematica
Time used: 0.099 (sec). Leaf size: 41
DSolve[y''[x]+16*y[x]==Sin[4*x+\[Alpha]],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{64} \sin (\alpha +4 x)-\frac {1}{8} x \cos (\alpha +4 x)+c_1 \cos (4 x)+c_2 \sin (4 x) \]