ENGR201 Laplace deck example, solving a second order ODETutorialOld spec ENGR2012:212 minENGR201 (old spec) Laplace transforms deck, Laplace transforms of differential equations example (page 24)Solve, using Laplace transforms, d2ydt2+6dydt+8y=2,y(0)=y′(0)=0\frac{d^2y}{dt^2} + 6\frac{dy}{dt} + 8y = 2, \qquad y(0) = y'(0) = 0dt2d2y+6dtdy+8y=2,y(0)=y′(0)=0Formulas you may need L[y′]=sY−y(0)\mathcal{L}[y'] = sY - y(0)L[y′]=sY−y(0), L[y′′]=s2Y−sy(0)−y′(0)\mathcal{L}[y''] = s^2Y - sy(0) - y'(0)L[y′′]=s2Y−sy(0)−y′(0); constant c→c/sc \to c/sc→c/s; e−at↔1s+ae^{-at} \leftrightarrow \dfrac{1}{s + a}e−at↔s+a1 (learn this) (a)Find Y(s)Y(s)Y(s).(b)Find y(t)y(t)y(t) by partial fractions, and give y(1)y(1)y(1) and the final value.y(1) =Checky(infinity) =CheckShow worked solution