75.16.9 problem 482

Internal problem ID [16982]
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 : 482
Date solved : Tuesday, January 28, 2025 at 09:44:17 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+25 y&=\cos \left (5 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 27

dsolve(diff(y(x),x$2)+25*y(x)=cos(5*x),y(x), singsol=all)
 

\[ y = \frac {\left (50 c_{1} +1\right ) \cos \left (5 x \right )}{50}+\frac {\sin \left (5 x \right ) \left (x +10 c_{2} \right )}{10} \]

✓ Solution by Mathematica

Time used: 0.100 (sec). Leaf size: 64

DSolve[D[y[x],{x,2}]+25*y[x]==Cos[5*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sin (5 x) \int _1^x\frac {1}{5} \cos ^2(5 K[2])dK[2]+\cos (5 x) \int _1^x-\frac {1}{10} \sin (10 K[1])dK[1]+c_1 \cos (5 x)+c_2 \sin (5 x) \]