73.15.37 problem 22.10 (j)

Internal problem ID [15468]
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 (j)
Date solved : Tuesday, January 28, 2025 at 07:57:22 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&={\mathrm e}^{-x} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 27

dsolve(diff(y(x),x$2)-4*diff(y(x),x)+5*y(x)=exp(-x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{2 x} \sin \left (x \right ) c_{2} +{\mathrm e}^{2 x} \cos \left (x \right ) c_{1} +\frac {{\mathrm e}^{-x}}{10} \]

✓ Solution by Mathematica

Time used: 0.070 (sec). Leaf size: 63

DSolve[D[y[x],{x,2}]-4*D[y[x],x]+5*y[x]==Exp[-x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{2 x} \left (\cos (x) \int _1^x-e^{-3 K[2]} \sin (K[2])dK[2]+\sin (x) \int _1^xe^{-3 K[1]} \cos (K[1])dK[1]+c_2 \cos (x)+c_1 \sin (x)\right ) \]