Internal problem ID [11828]
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.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime \prime }+10 y^{\prime \prime }+9 y=\sin \left (x \right ) \sin \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (x \right ) = \frac {\left (11+1152 c_{3} \right ) \cos \left (3 x \right )}{1152}+\frac {\left (x +96 c_{4} \right ) \sin \left (3 x \right )}{96}+\frac {\left (-1+64 c_{1} \right ) \cos \left (x \right )}{64}+\frac {\sin \left (x \right ) \left (x +32 c_{2} \right )}{32} \]
✓ Solution by Mathematica
Time used: 0.079 (sec). Leaf size: 54
DSolve[y''''[x]+10*y''[x]+9*y[x]==Sin[x]*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{32} x \sin (x)+\frac {1}{96} x \sin (3 x)+\left (-\frac {1}{64}+c_3\right ) \cos (x)+\left (\frac {13}{576}+c_1\right ) \cos (3 x)+c_4 \sin (x)+c_2 \sin (3 x) \]