Differential equations Both a and b 7. Determine a continuous function / with L = F for 2-3s + 6: (a) (10 point) F(s) (b) (10 points) Flo) s + 2
differential equations s + 8 + 65 Find f(t). 25 + 7 الم f(t) =
differential equations Definition 7.1.1 Laplace Transform Let f be a function defined for t 2 0. Then the integral 00 L{f(t)} = -192 e-stf(t) dt is said to be the Laplace transform of f, provided that the integral converges. 16, f(t) = {6, ost<4 t24 Complete the integral(s) that defines L{f(t)}. L{f(t)} = Datet (" dt Find L{f(t)}. (Write your answer as a function of s.) L{f(t)} = (s > 0)
Question 3 Evaluate. 12 when 0<t<5 L {f(t) } where f(t) = 0 when 5<t<10 e4t when 10<t 0349
differential equations Use Definition 7.1.1. Definition 7.1.1 Laplace Transform Let f be a function defined for t 2 0. Then the integral **F¢)} = [" e stf(t) dt is said to be the Laplace transform of f, provided that the integral converges. 16, f(t) = Ost<4 t24 Complete the integral(s) that defines {f(t)}. {f(t)} = o Find L{f(t)}. (Write your answer as a function of s.) L{f(t)} = (s > 0)
Find the Inverse Transform L {F(s)} of F(s) 38+2 $2 -38 +2 o L 1{F(s)} = 8e2t - 5et OL-'{F(s)} 5 8-1 $ 2 L'{F(s)} = -5e2-8et None of them
Find the inverse Laplace transform of the function F(s) s +1 $2 - 8s + 20 * uz(t)e(4t-12) (cos(2t – 6) + 2.5 sin(2t – 6)) OF U3(t)e4t (cos(2t – 3) + 0.5 sin(2t – 3)) OC e(4t-12) (cos(2t – 3) + sin(2t – 3)) OD uz(t) (cos(2t – 6) + sin(2t – 6)) ОЕ uz(t) (e4t – 5t)
Find the Laplace transform of g(t)=e4t +5cos(3t) - e3tcos(6t). f(t)=7e-3t+4+? - 12 3 h(t)=(10) 2
2. Differential equations and direction fields (a) Find the general solution to the differential equation y' = 20e3+ + + (b) Find the particular solution to the initial value problem y' = 64 – 102, y(0) = 11. (e) List the equilibrium solutions of the differential equation V = (y2 - 1) arctan() (d) List all equilibrium solutions of the differential equation, and classify the stability of each: V = y(y - 6)(n-10) (e) Use equilibrium solutions and stability analysis...
- Find L-1{f(t)} f(t) s+2 s-(s + 1)2