Internal problem ID [13729]
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: 22.10 (g).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+5 y={\mathrm e}^{2 x} \sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 27
dsolve(diff(y(x),x$2)-4*diff(y(x),x)+5*y(x)=exp(2*x)*sin(x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\left (\left (x -2 c_{1} \right ) \cos \left (x \right )+\left (-2 c_{2} -1\right ) \sin \left (x \right )\right ) {\mathrm e}^{2 x}}{2} \]
✓ Solution by Mathematica
Time used: 0.052 (sec). Leaf size: 30
DSolve[y''[x]-4*y'[x]+5*y[x]==Exp[2*x]*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{2} e^{2 x} ((x-2 c_2) \cos (x)-2 c_1 \sin (x)) \]