Internal problem ID [15276]
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: 506.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime \prime }-2 n^{2} y^{\prime \prime }+n^{4} y=\cos \left (n x +\alpha \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 49
dsolve(diff(y(x),x$4)-2*n^2*diff(y(x),x$2)+n^4*y(x)=cos(n*x+alpha),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\cos \left (n x +\alpha \right )+\left (4 c_{4} x +4 c_{2} \right ) n^{4} {\mathrm e}^{-n x}+\left (4 c_{3} x +4 c_{1} \right ) n^{4} {\mathrm e}^{n x}}{4 n^{4}} \]
✓ Solution by Mathematica
Time used: 0.234 (sec). Leaf size: 52
DSolve[y''''[x]-2*n^2*y''[x]+n^4*y[x]==Cos[n*x+\[Alpha]],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {\cos (\alpha +n x)}{4 n^4}+e^{-n x} \left (c_3 e^{2 n x}+c_4 x e^{2 n x}+c_2 x+c_1\right ) \]