35.6.14 problem 14

Internal problem ID [6164]
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 : 14
Date solved : Monday, January 27, 2025 at 01:41:19 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+8 y^{\prime }+25 y&=120 \sin \left (5 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 31

dsolve(diff(y(x),x$2)+8*diff(y(x),x)+25*y(x)=120*sin(5*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 36

DSolve[D[y[x],{x,2}]+8*D[y[x],x]+25*y[x]==120*Sin[5*x],y[x],x,IncludeSingularSolutions -> True]
 

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