Internal problem ID [15300]
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: 530.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-2 m y^{\prime }+m^{2} y=\sin \left (n x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 56
dsolve(diff(y(x),x$2)-2*m*diff(y(x),x)+m^2*y(x)=sin(n*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (m^{2}+n^{2}\right )^{2} \left (c_{1} x +c_{2} \right ) {\mathrm e}^{m x}+\left (m^{2}-n^{2}\right ) \sin \left (n x \right )+2 \cos \left (n x \right ) m n}{\left (m^{2}+n^{2}\right )^{2}} \]
✓ Solution by Mathematica
Time used: 0.182 (sec). Leaf size: 56
DSolve[y''[x]-2*m*y'[x]+m^2*y[x]==Sin[n*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {\left (m^2-n^2\right ) \sin (n x)+2 m n \cos (n x)}{\left (m^2+n^2\right )^2}+c_1 e^{m x}+c_2 x e^{m x} \]