Internal problem ID [15277]
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: 507.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+6 y^{\prime \prime }+4 y^{\prime }+y=\sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(diff(y(x),x$4)+4*diff(y(x),x$3)+6*diff(y(x),x$2)+4*diff(y(x),x)+y(x)=sin(x),y(x), singsol=all)
\[ y \left (x \right ) = \left (c_{3} x^{3}+c_{2} x^{2}+c_{4} x +c_{1} \right ) {\mathrm e}^{-x}-\frac {\sin \left (x \right )}{4} \]
✓ Solution by Mathematica
Time used: 0.102 (sec). Leaf size: 35
DSolve[y''''[x]+4*y'''[x]+6*y''[x]+4*y'[x]+y[x]==Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {\sin (x)}{4}+e^{-x} (x (x (c_4 x+c_3)+c_2)+c_1) \]