32.8.9 problem Exercise 21.11, page 231

Internal problem ID [5958]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 4. Higher order linear differential equations. Lesson 21. Undetermined Coefficients
Problem number : Exercise 21.11, page 231
Date solved : Monday, January 27, 2025 at 01:28:53 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }&=2 \,{\mathrm e}^{2 x} \sin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 28

dsolve(diff(y(x),x$2)-3*diff(y(x),x)=2*exp(2*x)*sin(x),y(x), singsol=all)
 

\[ y \left (x \right ) = c_{2} +\frac {c_{1} {\mathrm e}^{3 x}}{3}+\frac {{\mathrm e}^{2 x} \left (-\cos \left (x \right )-3 \sin \left (x \right )\right )}{5} \]

✓ Solution by Mathematica

Time used: 0.229 (sec). Leaf size: 33

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

\[ y(x)\to \frac {1}{15} e^{2 x} \left (-9 \sin (x)-3 \cos (x)+5 c_1 e^x\right )+c_2 \]