Laplace Transform Cheat Sheet - F(t) l[f](s) 1 1 s t 1 s2 ert 1 s r cos t s s2+ 2 sin t s 2+ e tcos( t) s (s )2+ 2 e tsin( t) (s )2+ 2 eatf(t) l[f](s a) f(t c)u c(t) e csl[f](s) f(t c)h(t c) e csl[f](s) (t c) e cs z t 0 f(t ˝)g(˝)d˝ l[f](s)l[g](s) f0(t) sl[f](s) f(0) f00(t) s2l[f](s) sf(0) f0(0) tf(t) d ds (l[f](s)) tert 1 (s r)2 tsin( t. Web math 3d laplace transform cheat sheet (spring 2017) aaron chen common forwards (and hence, backwards) transforms on pg 269. (b) use rules and solve: Solve y00 + y = u5(t) with y(0) = 0 and y0(0) = 3, using the laplace transform. Solve y00 y = e2t with y(0) = 0 and y0(0) = 1, using the laplace transform. Solve y′′+ 3y′−4y= 0 with y(0) = 0 and y′(0) = 6, using the laplace transform. 4y = 0 with y(0) = 0 and y0(0) = 6, using the laplace transform. Lfeatg= 1 s+a lfsin(wt)g= w s2+w2. (s2 + 3s−4)l{y}−6 = 0. Web list of laplace transform formulas:
Solve y00 + y = u5(t) with y(0) = 0 and y0(0) = 3, using the laplace transform. Solve y′′+ 3y′−4y= 0 with y(0) = 0 and y′(0) = 6, using the laplace transform. S2l{y}−sy(0) −y′(0) + 3sl{y}−3y(0) −4l{y}= 0, which becomes: Solve y00 + 2y + y = 0 with y(0) = 3 and y0(0) = 1, using the laplace transform. 4y = 0 with y(0) = 0 and y0(0) = 6, using the laplace transform. Web list of laplace transform formulas: (b) use rules and solve: Web math 3d laplace transform cheat sheet (spring 2017) aaron chen common forwards (and hence, backwards) transforms on pg 269. F(t) l[f](s) 1 1 s t 1 s2 ert 1 s r cos t s s2+ 2 sin t s 2+ e tcos( t) s (s )2+ 2 e tsin( t) (s )2+ 2 eatf(t) l[f](s a) f(t c)u c(t) e csl[f](s) f(t c)h(t c) e csl[f](s) (t c) e cs z t 0 f(t ˝)g(˝)d˝ l[f](s)l[g](s) f0(t) sl[f](s) f(0) f00(t) s2l[f](s) sf(0) f0(0) tf(t) d ds (l[f](s)) tert 1 (s r)2 tsin( t. Lfeatg= 1 s+a lfsin(wt)g= w s2+w2. (s2 + 3s−4)l{y}−6 = 0. Solve y00 y = e2t with y(0) = 0 and y0(0) = 1, using the laplace transform.