Internal problem ID [11798]
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: 24.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+7 y^{\prime \prime }-5 y^{\prime }+6 y=5 \sin \left (x \right )-12 \sin \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 51
dsolve(diff(y(x),x$4)-5*diff(y(x),x$3)+7*diff(y(x),x$2)-5*diff(y(x),x)+6*y(x)=5*sin(x)-12*sin(2*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {5 \cos \left (2 x \right )}{13}+c_{3} {\mathrm e}^{2 x}+c_{4} {\mathrm e}^{3 x}+\frac {\sin \left (2 x \right )}{13}+\frac {\left (-2-5 x +20 c_{1} \right ) \cos \left (x \right )}{20}+\frac {\left (1+x +4 c_{2} \right ) \sin \left (x \right )}{4} \]
✓ Solution by Mathematica
Time used: 0.232 (sec). Leaf size: 71
DSolve[y''''[x]-5*y'''[x]+7*y''[x]-5*y'[x]+6*y[x]==5*Sin[x]-12*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {5 \sin ^2(x)}{13}+\frac {5 \cos ^2(x)}{13}+e^{2 x} \left (c_4 e^x+c_3\right )+\left (\frac {x}{4}+\frac {3}{8}+c_2\right ) \sin (x)+\cos (x) \left (-\frac {x}{4}+\frac {2 \sin (x)}{13}-\frac {1}{10}+c_1\right ) \]