Internal problem ID [4318]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+4 y^{\prime }+8 y-30 \,{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {5 x}{2}\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (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)
\[ y \relax (x ) = {\mathrm e}^{-2 x} \sin \left (2 x \right ) c_{2}+{\mathrm e}^{-2 x} \cos \left (2 x \right ) c_{1}+4 \,{\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {5 x}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.146 (sec). Leaf size: 41
DSolve[y''[x]+4*y'[x]+8*y[x]==30*Exp[-x/2]*Cos[5/2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} 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 ) \\ \end{align*}