Internal problem ID [5746]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 7. Laplace Transforms. Section 7.5 The Unit Step and Impulse Functions. Page
303
Problem number: 1(a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+5 y^{\prime }+6 y-5 \,{\mathrm e}^{3 t}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 20
dsolve([diff(y(t),t$2)+5*diff(y(t),t)+6*y(t)=5*exp(3*t),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \relax (t ) = \frac {\left ({\mathrm e}^{6 t}-6 \,{\mathrm e}^{t}+5\right ) {\mathrm e}^{-3 t}}{6} \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 26
DSolve[{y''[t]+5*y'[t]+6*y[t]==5*Exp[3*t],{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{6} e^{-3 t} \left (-6 e^t+e^{6 t}+5\right ) \\ \end{align*}