Internal problem ID [15274]
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: 504.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime \prime }+4 y^{\prime \prime }+4 y=x \sin \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 40
dsolve(diff(y(x),x$4)+4*diff(y(x),x$2)+4*y(x)=x*sin(2*x),y(x), singsol=all)
\[ y \left (x \right ) = \left (c_{3} x +c_{1} \right ) \cos \left (\sqrt {2}\, x \right )+\left (c_{4} x +c_{2} \right ) \sin \left (\sqrt {2}\, x \right )+\frac {x \sin \left (2 x \right )}{4}+\cos \left (2 x \right ) \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 58
DSolve[y''''[x]+4*y''[x]+4*y[x]==x*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} x \sin (2 x)+\cos (2 x)+(c_2 x+c_1) \cos \left (\sqrt {2} x\right )+c_3 \sin \left (\sqrt {2} x\right )+c_4 x \sin \left (\sqrt {2} x\right ) \]