Internal problem ID [13213]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 14. Higher order equations and the reduction of order method. Additional
exercises page 277
Problem number: 14.1 (h).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+5 y=30 \,{\mathrm e}^{3 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(diff(y(x),x$2)=2*diff(y(x),x)-5*y(x)+30*exp(3*x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{x} \sin \left (2 x \right ) c_{2} +{\mathrm e}^{x} \cos \left (2 x \right ) c_{1} +\frac {15 \,{\mathrm e}^{3 x}}{4} \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 35
DSolve[y''[x]==2*y'[x]-5*y[x]+30*Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {15 e^{3 x}}{4}+c_2 e^x \cos (2 x)+c_1 e^x \sin (2 x) \]