Internal problem ID [4316]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+2 y^{\prime }+17 y-60 \,{\mathrm e}^{-4 x} \sin \left (5 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \relax (x ) = {\mathrm e}^{-x} \sin \left (4 x \right ) c_{2}+{\mathrm e}^{-x} \cos \left (4 x \right ) c_{1}+2 \,{\mathrm e}^{-4 x} \cos \left (5 x \right ) \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 38
DSolve[y''[x]+2*y'[x]+17*y[x]==60*Exp[-4*x]*Sin[5*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2 e^{-4 x} \cos (5 x)+e^{-x} (c_2 \cos (4 x)+c_1 \sin (4 x)) \\ \end{align*}