73.17.34 problem 34

Internal problem ID [15568]
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 : 34
Date solved : Tuesday, January 28, 2025 at 08:02:17 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-12 y^{\prime }+36 y&=81 \,{\mathrm e}^{3 x} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 21

dsolve(diff(y(x),x$2)-12*diff(y(x),x)+36*y(x)=81*exp(3*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 26

DSolve[D[y[x],{x,2}]-12*D[y[x],x]+36*y[x]==81*Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{3 x} \left (9+e^{3 x} (c_2 x+c_1)\right ) \]