73.9.8 problem 14.1 (h)

Internal problem ID [15269]
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)
Date solved : Tuesday, January 28, 2025 at 07:51:13 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }&=2 y^{\prime }-5 y+30 \,{\mathrm e}^{3 x} \end{align*}

✓ Solution by Maple

Time used: 0.006 (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)
 

\[ y = {\mathrm e}^{x} \sin \left (2 x \right ) c_{2} +{\mathrm e}^{x} \cos \left (2 x \right ) c_{1} +\frac {15 \,{\mathrm e}^{3 x}}{4} \]

✓ Solution by Mathematica

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

DSolve[D[y[x],{x,2}]==2*D[y[x],x]-5*y[x]+30*Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {15 e^{3 x}}{4}+c_2 e^x \cos (2 x)+c_1 e^x \sin (2 x) \]