Internal problem ID [4648]
Book: Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY.
2001
Section: Program 25. Second order differential equations. Further problems 25. page 1094
Problem number: 14.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {x^{\prime \prime }-3 x^{\prime }+2 x-\sin \relax (t )=0} \end {gather*} With initial conditions \begin {align*} [x \relax (0) = 0, x^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.012 (sec). Leaf size: 23
dsolve([diff(x(t),t$2)-3*diff(x(t),t)+2*x(t)=sin(t),x(0) = 0, D(x)(0) = 0],x(t), singsol=all)
\[ x \relax (t ) = \frac {{\mathrm e}^{2 t}}{5}+\frac {3 \cos \relax (t )}{10}+\frac {\sin \relax (t )}{10}-\frac {{\mathrm e}^{t}}{2} \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 27
DSolve[{x''[t]-3*x'[t]+2*x[t]==Sin[t],{x[0]==0,x'[0]==0}},x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{10} \left (e^t \left (2 e^t-5\right )+\sin (t)+3 \cos (t)\right ) \\ \end{align*}