64.11.54 problem 54

Internal problem ID [13504]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.3. The method of undetermined coefficients. Exercises page 151
Problem number : 54
Date solved : Tuesday, January 28, 2025 at 05:50:06 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }+10 y^{\prime \prime }+9 y&=\sin \left (x \right ) \sin \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 45

dsolve(diff(y(x),x$4)+10*diff(y(x),x$2)+9*y(x)=sin(x)*sin(2*x),y(x), singsol=all)
 

\[ y = \frac {\left (11+1152 c_{3} \right ) \cos \left (3 x \right )}{1152}+\frac {\left (x +96 c_4 \right ) \sin \left (3 x \right )}{96}+\frac {\left (-1+64 c_{1} \right ) \cos \left (x \right )}{64}+\frac {\sin \left (x \right ) \left (x +32 c_{2} \right )}{32} \]

✓ Solution by Mathematica

Time used: 0.120 (sec). Leaf size: 129

DSolve[D[y[x],{x,4}]+10*D[y[x],{x,2}]+9*y[x]==Sin[x]*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sin (x) \int _1^x\frac {1}{16} \sin ^2(2 K[3])dK[3]+\sin (3 x) \int _1^x-\frac {1}{12} \cos ^2(K[2]) (2 \cos (2 K[2])-1) \sin ^2(K[2])dK[2]+\cos (3 x) \int _1^x\frac {1}{12} \cos (K[1]) (2 \cos (2 K[1])+1) \sin ^3(K[1])dK[1]-\frac {1}{16} \sin ^4(x) \cos (x)+c_3 \cos (x)+c_1 \cos (3 x)+c_4 \sin (x)+c_2 \sin (3 x) \]