Internal problem ID [13832]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-12 y^{\prime }+36 y=81 \,{\mathrm e}^{3 x}} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = \left (c_{1} x +c_{2} \right ) {\mathrm e}^{6 x}+9 \,{\mathrm e}^{3 x} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 26
DSolve[y''[x]-12*y'[x]+36*y[x]==81*Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{3 x} \left (9+e^{3 x} (c_2 x+c_1)\right ) \]