73.15.70 problem 22.14 (a)

Internal problem ID [15501]
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 : 22.14 (a)
Date solved : Tuesday, January 28, 2025 at 07:59:48 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=27 \,{\mathrm e}^{6 x}+25 \sin \left (6 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 33

dsolve(diff(y(x),x$2)-6*diff(y(x),x)+9*y(x)=27*exp(6*x)+25*sin(6*x),y(x), singsol=all)
 

\[ y = \left (c_{1} x +c_{2} \right ) {\mathrm e}^{3 x}+\frac {4 \cos \left (6 x \right )}{9}+3 \,{\mathrm e}^{6 x}-\frac {\sin \left (6 x \right )}{3} \]

✓ Solution by Mathematica

Time used: 0.439 (sec). Leaf size: 82

DSolve[D[y[x],{x,2}]-6*D[y[x],x]+9*y[x]==27*Exp[6*x]+25*Sin[6*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{3 x} \left (\int _1^x-e^{-3 K[1]} K[1] \left (25 \sin (6 K[1])+27 e^{6 K[1]}\right )dK[1]+x \int _1^x\left (25 e^{-3 K[2]} \sin (6 K[2])+27 e^{3 K[2]}\right )dK[2]+c_2 x+c_1\right ) \]