Internal problem ID [13410]
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 (h).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+5 y={\mathrm e}^{-x} \sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 36
dsolve(diff(y(x),x$2)-4*diff(y(x),x)+5*y(x)=exp(-x)*sin(x),y(x), singsol=all)
\[ y = {\mathrm e}^{2 x} \sin \left (x \right ) c_{2} +{\mathrm e}^{2 x} \cos \left (x \right ) c_{1} +\frac {{\mathrm e}^{-x} \left (3 \sin \left (x \right )+2 \cos \left (x \right )\right )}{39} \]
✓ Solution by Mathematica
Time used: 0.16 (sec). Leaf size: 44
DSolve[y''[x]-4*y'[x]+5*y[x]==Exp[-x]*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{78} e^{-x} \left (\left (4+78 c_2 e^{3 x}\right ) \cos (x)+6 \left (1+13 c_1 e^{3 x}\right ) \sin (x)\right ) \]