75.16.31 problem 504

Internal problem ID [17004]
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 ODEs). Section 15.3 Nonhomogeneous linear equations with constant coefficients. Trial and error method. Exercises page 132
Problem number : 504
Date solved : Tuesday, January 28, 2025 at 09:45:24 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime }+4 y&=x \sin \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (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)
 

\[ y = \left (c_{3} x +c_{1} \right ) \cos \left (\sqrt {2}\, x \right )+\left (c_4 x +c_{2} \right ) \sin \left (\sqrt {2}\, x \right )+\frac {x \sin \left (2 x \right )}{4}+\cos \left (2 x \right ) \]

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 58

DSolve[D[y[x],{x,4}]+4*D[y[x],{x,2}]+4*y[x]==x*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{4} x \sin (2 x)+\cos (2 x)+(c_2 x+c_1) \cos \left (\sqrt {2} x\right )+c_3 \sin \left (\sqrt {2} x\right )+c_4 x \sin \left (\sqrt {2} x\right ) \]