Internal problem ID [5154]
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: 12.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{\prime \prime }+4 x^{\prime }+3 x={\mathrm e}^{-3 t}} \] With initial conditions \begin {align*} \left [x \left (0\right ) = {\frac {1}{2}}, x^{\prime }\left (0\right ) = -2\right ] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 13
dsolve([diff(x(t),t$2)+4*diff(x(t),t)+3*x(t)=exp(-3*t),x(0) = 1/2, D(x)(0) = -2],x(t), singsol=all)
\[ x \left (t \right ) = -\frac {{\mathrm e}^{-3 t} \left (t -1\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.034 (sec). Leaf size: 17
DSolve[{x''[t]+4*x'[t]+3*x[t]==Exp[-3*t],{x[0]==1/2,x'[0]==-2}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to -\frac {1}{2} e^{-3 t} (t-1) \]