73.15.17 problem 22.7 (b)

Internal problem ID [15448]
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 : 22.7 (b)
Date solved : Tuesday, January 28, 2025 at 07:56:11 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{2 x} \sin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

dsolve(diff(y(x),x$2)-6*diff(y(x),x)+9*y(x)=exp(2*x)*sin(x),y(x), singsol=all)
 

\[ y = \left (c_{1} x +c_{2} \right ) {\mathrm e}^{3 x}+\frac {{\mathrm e}^{2 x} \cos \left (x \right )}{2} \]

✓ Solution by Mathematica

Time used: 0.097 (sec). Leaf size: 57

DSolve[D[y[x],{x,2}]-6*D[y[x],x]+9*y[x]==Exp[2*x]*Sin[x],y[x],x,IncludeSingularSolutions -> True]
 

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