Internal problem ID [4309]
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: 12.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y^{\prime }+12 y-80 \sin \left (2 x \right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 43
dsolve(diff(y(x),x$2)+4*diff(y(x),x)+12*y(x)=80*sin(2*x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-2 x} \sin \left (2 \sqrt {2}\, x \right ) c_{2} +{\mathrm e}^{-2 x} \cos \left (2 \sqrt {2}\, x \right ) c_{1} +5 \sin \left (2 x \right )-5 \cos \left (2 x \right ) \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 49
DSolve[y''[x]+4*y'[x]+12*y[x]==80*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 5 \sin (2 x)-5 \cos (2 x)+e^{-2 x} \left (c_2 \cos \left (2 \sqrt {2} x\right )+c_1 \sin \left (2 \sqrt {2} x\right )\right ) \\ \end{align*}