Internal problem ID [5905]
Book: DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL,
WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th
edition.
Section: CHAPTER 7 THE LAPLACE TRANSFORM. 7.2.2 TRANSFORMS OF DERIVATIVES
Page 289
Problem number: 33.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {y^{\prime }+6 y-{\mathrm e}^{4 t}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 16
dsolve([diff(y(t),t)+6*y(t)=exp(4*t),y(0) = 2],y(t), singsol=all)
\[ y \relax (t ) = \frac {\left ({\mathrm e}^{10 t}+19\right ) {\mathrm e}^{-6 t}}{10} \]
✓ Solution by Mathematica
Time used: 0.079 (sec). Leaf size: 21
DSolve[{y'[t]+6*y[t]==Exp[4*t],{y[0]==2}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{10} e^{-6 t} \left (e^{10 t}+19\right ) \\ \end{align*}