Internal problem ID [4313]
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: 15.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {5 y^{\prime \prime }+12 y^{\prime }+20 y-120 \sin \left (2 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(5*diff(y(x),x$2)+12*diff(y(x),x)+20*y(x)=120*sin(2*x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-\frac {6 x}{5}} \sin \left (\frac {8 x}{5}\right ) c_{2}+{\mathrm e}^{-\frac {6 x}{5}} \cos \left (\frac {8 x}{5}\right ) c_{1}-5 \cos \left (2 x \right ) \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 39
DSolve[5*y''[x]+12*y'[x]+20*y[x]==120*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -5 \cos (2 x)+e^{-6 x/5} \left (c_2 \cos \left (\frac {8 x}{5}\right )+c_1 \sin \left (\frac {8 x}{5}\right )\right ) \\ \end{align*}