6.2 problem 22

Internal problem ID [5916]

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. 7.3.1 TRANSLATION ON THE s-AXIS. Page 297
Problem number: 22.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_linear, class A]]

Solve \begin {gather*} \boxed {y^{\prime }-y-1-{\mathrm e}^{t} t=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0] \end {align*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 20

dsolve([diff(y(t),t)-y(t)=1+t*exp(t),y(0) = 0],y(t), singsol=all)
 

\[ y \relax (t ) = \frac {{\mathrm e}^{t} t^{2}}{2}-1+{\mathrm e}^{t} \]

Solution by Mathematica

Time used: 0.083 (sec). Leaf size: 19

DSolve[{y'[t]-y[t]==1+t*Exp[t],{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to \frac {1}{2} e^t \left (t^2+2\right )-1 \\ \end{align*}