Internal problem ID [15252]
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: 482.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+25 y=\cos \left (5 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(diff(y(x),x$2)+25*y(x)=cos(5*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (50 c_{1} +1\right ) \cos \left (5 x \right )}{50}+\frac {\sin \left (5 x \right ) \left (x +10 c_{2} \right )}{10} \]
✓ Solution by Mathematica
Time used: 0.097 (sec). Leaf size: 31
DSolve[y''[x]+25*y[x]==Cos[5*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \left (\frac {1}{100}+c_1\right ) \cos (5 x)+\frac {1}{10} (x+10 c_2) \sin (5 x) \]