Internal problem ID [2749]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }+5 y=3 \sin \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \left (x \right ) = \frac {\sin \left (2 x \right ) \left (17 \,{\mathrm e}^{-x} c_{2} +3\right )}{17}+\cos \left (2 x \right ) {\mathrm e}^{-x} c_{1} -\frac {12 \cos \left (2 x \right )}{17} \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 45
DSolve[y''[x]+2*y'[x]+5*y[x]==3*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{17} e^{-x} \left (\left (-12 e^x+17 c_2\right ) \cos (2 x)+\left (3 e^x+17 c_1\right ) \sin (2 x)\right ) \]