Internal problem ID [11825]
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: 51.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y=\cos \left (x \right ) x^{2}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 46
dsolve(diff(y(x),x$4)+2*diff(y(x),x$2)+y(x)=x^2*cos(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (-4 x^{4}+192 c_{4} x +36 x^{2}+192 c_{1} -21\right ) \cos \left (x \right )}{192}+\frac {\left (x^{3}+\left (12 c_{3} -3\right ) x +12 c_{2} \right ) \sin \left (x \right )}{12} \]
✓ Solution by Mathematica
Time used: 0.138 (sec). Leaf size: 56
DSolve[y''''[x]+2*y''[x]+y[x]==x^2*Cos[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{12} \left (x^3+3 (-1+4 c_4) x+12 c_3\right ) \sin (x)+\left (-\frac {x^4}{48}+\frac {3 x^2}{16}+c_2 x-\frac {5}{32}+c_1\right ) \cos (x) \]