35.6.20 problem 20

Internal problem ID [6170]
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 : 20
Date solved : Monday, January 27, 2025 at 01:44:55 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }+8 y&=30 \,{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {5 x}{2}\right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 35

dsolve(diff(y(x),x$2)+4*diff(y(x),x)+8*y(x)=30*exp(-x/2)*cos(5/2*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 41

DSolve[D[y[x],{x,2}]+4*D[y[x],x]+8*y[x]==30*Exp[-x/2]*Cos[5/2*x],y[x],x,IncludeSingularSolutions -> True]
 

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