Internal problem ID [13427]
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 (k).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+20 y={\mathrm e}^{2 x} \sin \left (4 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 36
dsolve(diff(y(x),x$2)-4*diff(y(x),x)+20*y(x)=exp(2*x)*sin(4*x),y(x), singsol=all)
\[ y = {\mathrm e}^{2 x} \sin \left (4 x \right ) c_{2} +{\mathrm e}^{2 x} \cos \left (4 x \right ) c_{1} -\frac {{\mathrm e}^{2 x} \cos \left (4 x \right ) x}{8} \]
✓ Solution by Mathematica
Time used: 0.116 (sec). Leaf size: 38
DSolve[y''[x]-4*y'[x]+20*y[x]==Exp[2*x]*Sin[4*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{64} e^{2 x} ((1+64 c_1) \sin (4 x)-8 (x-8 c_2) \cos (4 x)) \]