Internal problem ID [11823]
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: 49.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime \prime }-16 y=x^{2} \sin \left (2 x \right )+{\mathrm e}^{2 x} x^{4}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 79
dsolve(diff(y(x),x$4)-16*y(x)=x^2*sin(2*x)+x^4*exp(2*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (128 x^{5}-480 x^{4}+800 x^{3}-600 x^{2}+20480 c_{3} +60 x +105\right ) {\mathrm e}^{2 x}}{20480}+\frac {\left (8 x^{3}+768 c_{1} -15 x \right ) \cos \left (2 x \right )}{768}+\frac {\left (-6 x^{2}+256 c_{4} -11\right ) \sin \left (2 x \right )}{256}+{\mathrm e}^{-2 x} c_{2} \]
✓ Solution by Mathematica
Time used: 0.562 (sec). Leaf size: 92
DSolve[y''''[x]-16*y[x]==x^2*Sin[2*x]+x^4*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{768} \left (8 x^3-15 x+768 c_2\right ) \cos (2 x)-\frac {1}{512} \left (24 x^2-5-1024 c_4\right ) \sin (x) \cos (x)+\frac {e^{2 x} \left (128 x^5-480 x^4+800 x^3-600 x^2+60 x+105+20480 c_1\right )}{20480}+c_3 e^{-2 x} \]