7.11.28 problem 28

Internal problem ID [349]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.5 (Nonhomogeneous equations and undetermined coefficients). Problems at page 161
Problem number : 28
Date solved : Wednesday, February 05, 2025 at 03:24:18 AM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime \prime }+9 y^{\prime \prime }&=\left (x^{2}+1\right ) \sin \left (3 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 41

dsolve(diff(y(x),x$4)+9*diff(y(x),x$2)=(x^2+1)*sin(3*x),y(x), singsol=all)
 

\[ y = \frac {\left (6 x^{3}-108 c_1 +x \right ) \cos \left (3 x \right )}{972}+\frac {\left (-45 x^{2}-324 c_2 -11\right ) \sin \left (3 x \right )}{2916}+x c_3 +c_4 \]

✓ Solution by Mathematica

Time used: 0.777 (sec). Leaf size: 51

DSolve[D[y[x],{x,4}]+9*D[y[x],{x,2}]==(x^2+1)*Sin[3*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {6 \left (6 x^3+x-108 c_1\right ) \cos (3 x)-\left (90 x^2+41+648 c_2\right ) \sin (3 x)}{5832}+c_4 x+c_3 \]