Internal problem ID [13704]
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: 22.3 (d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y^{\prime }-5 y=\cos \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 32
dsolve(diff(y(x),x$2)+4*diff(y(x),x)-5*y(x)=cos(x),y(x), singsol=all)
\[ y \left (x \right ) = \left (\frac {\left (-3 \cos \left (x \right )+2 \sin \left (x \right )\right ) {\mathrm e}^{5 x}}{26}+c_{1} +{\mathrm e}^{6 x} c_{2} \right ) {\mathrm e}^{-5 x} \]
✓ Solution by Mathematica
Time used: 0.066 (sec). Leaf size: 32
DSolve[y''[x]+4*y'[x]-5*y[x]==Cos[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {\sin (x)}{13}-\frac {3 \cos (x)}{26}+c_1 e^{-5 x}+c_2 e^x \]