75.16.11 problem 484

Internal problem ID [16984]
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 ODEs). Section 15.3 Nonhomogeneous linear equations with constant coefficients. Trial and error method. Exercises page 132
Problem number : 484
Date solved : Tuesday, January 28, 2025 at 09:44:24 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+16 y&=\sin \left (4 x +\alpha \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 34

dsolve(diff(y(x),x$2)+16*y(x)=sin(4*x+alpha),y(x), singsol=all)
 

\[ y = c_{2} \sin \left (4 x \right )+c_{1} \cos \left (4 x \right )-\frac {x \cos \left (4 x +\alpha \right )}{8}+\frac {\sin \left (4 x +\alpha \right )}{64} \]

✓ Solution by Mathematica

Time used: 0.161 (sec). Leaf size: 76

DSolve[D[y[x],{x,2}]+16*y[x]==Sin[4*x+\[Alpha]],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \cos (4 x) \int _1^x-\frac {1}{4} \sin (4 K[1]) \sin (\alpha +4 K[1])dK[1]+\sin (4 x) \int _1^x\frac {1}{4} \cos (4 K[2]) \sin (\alpha +4 K[2])dK[2]+c_1 \cos (4 x)+c_2 \sin (4 x) \]