Internal problem ID [4312]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+8 y^{\prime }+25 y-120 \sin \left (5 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (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)
\[ y \relax (x ) = {\mathrm e}^{-4 x} \sin \left (3 x \right ) c_{2}+{\mathrm e}^{-4 x} \cos \left (3 x \right ) c_{1}-3 \cos \left (5 x \right ) \]
✓ Solution by Mathematica
Time used: 0.143 (sec). Leaf size: 33
DSolve[y''[x]+8*y'[x]+25*y[x]==120*Sin[5*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -3 \cos (5 x)+e^{-4 x} (c_2 \cos (3 x)+c_1 \sin (3 x)) \\ \end{align*}