73.15.34 problem 22.10 (g)

Internal problem ID [15465]
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)
Date solved : Tuesday, January 28, 2025 at 07:57:05 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&={\mathrm e}^{2 x} \sin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (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)
 

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

✓ Solution by Mathematica

Time used: 0.044 (sec). Leaf size: 53

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

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