35.6.18 problem 18

Internal problem ID [6168]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 6. SECOND-ORDER LINEAR EQUATIONSWITH CONSTANT COEFFICIENTS AND RIGHT-HAND SIDE NOT ZERO. page 422
Problem number : 18
Date solved : Monday, January 27, 2025 at 01:43:31 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+17 y&=60 \,{\mathrm e}^{-4 x} \sin \left (5 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 35

dsolve(diff(y(x),x$2)+2*diff(y(x),x)+17*y(x)=60*exp(-4*x)*sin(5*x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{-x} \sin \left (4 x \right ) c_2 +{\mathrm e}^{-x} \cos \left (4 x \right ) c_1 +2 \,{\mathrm e}^{-4 x} \cos \left (5 x \right ) \]

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 42

DSolve[D[y[x],{x,2}]+2*D[y[x],x]+17*y[x]==60*Exp[-4*x]*Sin[5*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-4 x} \left (2 \cos (5 x)+c_2 e^{3 x} \cos (4 x)+c_1 e^{3 x} \sin (4 x)\right ) \]