20.7.5 problem Problem 29

Internal problem ID [3720]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 8, Linear differential equations of order n. Section 8.3, The Method of Undetermined Coefficients. page 525
Problem number : Problem 29
Date solved : Monday, January 27, 2025 at 07:55:59 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=3 \sin \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 36

dsolve(diff(y(x),x$2)+2*diff(y(x),x)+5*y(x)=3*sin(2*x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\sin \left (2 x \right ) \left (17 c_{2} {\mathrm e}^{-x}+3\right )}{17}+{\mathrm e}^{-x} \cos \left (2 x \right ) c_{1} -\frac {12 \cos \left (2 x \right )}{17} \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 45

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

\[ y(x)\to \frac {1}{17} e^{-x} \left (\left (-12 e^x+17 c_2\right ) \cos (2 x)+\left (3 e^x+17 c_1\right ) \sin (2 x)\right ) \]