Internal problem ID [265]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.6, Forced Oscillations and Resonance. Page 362
Problem number: 9.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {2 x^{\prime \prime }+2 x^{\prime }+x-3 \sin \left (10 t \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 37
dsolve(2*diff(x(t),t$2)+2*diff(x(t),t)+x(t)=3*sin(10*t),x(t), singsol=all)
\[ x \relax (t ) = {\mathrm e}^{-\frac {t}{2}} \sin \left (\frac {t}{2}\right ) c_{2}+{\mathrm e}^{-\frac {t}{2}} \cos \left (\frac {t}{2}\right ) c_{1}-\frac {597 \sin \left (10 t \right )}{40001}-\frac {60 \cos \left (10 t \right )}{40001} \]
✓ Solution by Mathematica
Time used: 0.166 (sec). Leaf size: 50
DSolve[2*x''[t]+2*x'[t]+x[t]==3*Sin[10*t],x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -\frac {3 (199 \sin (10 t)+20 \cos (10 t))}{40001}+e^{-t/2} \left (c_2 \cos \left (\frac {t}{2}\right )+c_1 \sin \left (\frac {t}{2}\right )\right ) \\ \end{align*}