Internal problem ID [13746]
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 (j).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+20 y={\mathrm e}^{4 x} \sin \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 40
dsolve(diff(y(x),x$2)-4*diff(y(x),x)+20*y(x)=exp(4*x)*sin(2*x),y(x), singsol=all)
\[ y \left (x \right ) = \left (c_{1} \cos \left (4 x \right )+c_{2} \sin \left (4 x \right )\right ) {\mathrm e}^{2 x}-\frac {{\mathrm e}^{4 x} \left (\cos \left (2 x \right )-2 \sin \left (2 x \right )\right )}{40} \]
✓ Solution by Mathematica
Time used: 0.224 (sec). Leaf size: 54
DSolve[y''[x]-4*y'[x]+20*y[x]==Exp[4*x]*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{40} e^{2 x} \left (e^{2 x} \cos (2 x)-2 \left (e^{2 x} \sin (2 x)+20 c_2 \cos (4 x)+20 c_1 \sin (4 x)\right )\right ) \]