Internal problem ID [15302]
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: 532.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+a^{2} y=2 \cos \left (m x \right )+3 \sin \left (m x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 42
dsolve(diff(y(x),x$2)+a^2*y(x)=2*cos(m*x)+3*sin(m*x),y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (a x \right ) c_{2} +\cos \left (a x \right ) c_{1} +\frac {2 \cos \left (m x \right )+3 \sin \left (m x \right )}{a^{2}-m^{2}} \]
✓ Solution by Mathematica
Time used: 0.037 (sec). Leaf size: 45
DSolve[y''[x]+a^2*y[x]==2*Cos[m*x]+3*Sin[m*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {3 \sin (m x)+2 \cos (m x)}{a^2-m^2}+c_1 \cos (a x)+c_2 \sin (a x) \]