73.17.32 problem 32

Internal problem ID [15566]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 25. Review exercises for part III. page 447
Problem number : 32
Date solved : Tuesday, January 28, 2025 at 08:02:13 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-12 y^{\prime }+36 y&=25 \sin \left (3 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 27

dsolve(diff(y(x),x$2)-12*diff(y(x),x)+36*y(x)=25*sin(3*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 35

DSolve[D[y[x],{x,2}]-12*D[y[x],x]+36*y[x]==25*Sin[3*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{3} \sin (3 x)+\frac {4}{9} \cos (3 x)+e^{6 x} (c_2 x+c_1) \]