Internal problem ID [13428]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 22. Method of undetermined coefficients. Additional exercises page
412
Problem number: 22.11 (L).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+20 y=x^{3} \sin \left (4 x \right )} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 65
dsolve(diff(y(x),x$2)-4*diff(y(x),x)+20*y(x)=x^3*sin(4*x),y(x), singsol=all)
\[ y = {\mathrm e}^{2 x} \sin \left (4 x \right ) c_{2} +{\mathrm e}^{2 x} \cos \left (4 x \right ) c_{1} +\frac {\left (9826 x^{3}+16473 x^{2}+15810 x +7815\right ) \cos \left (4 x \right )}{167042}+\frac {\left (x^{3}+\frac {3}{17} x^{2}-\frac {39}{578} x -\frac {45}{4913}\right ) \sin \left (4 x \right )}{68} \]
✓ Solution by Mathematica
Time used: 0.041 (sec). Leaf size: 76
DSolve[y''[x]-4*y'[x]+20*y[x]==x^3*Sin[4*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {\left (9826 x^3+1734 x^2-663 x-90\right ) \sin (4 x)+4 \left (9826 x^3+16473 x^2+15810 x+7815\right ) \cos (4 x)}{668168}+c_2 e^{2 x} \cos (4 x)+c_1 e^{2 x} \sin (4 x) \]