Chapter 1.1, Problem 9E

Inverse laplace transform Lect :Huda I H.w A- Find L-1 F(s) of the following 1- F(S)= 2- F(s)- S (+1)5 s² (s-a) 5+5 s2+4s+3 3- F(s)- 1 4- F(s)- (s+2)2(s-2) 3s2-7s+5 5- F(s)- (s-1)(s2-55+6) B-Solve the D.E of the following: 1- y'+3y+2fy dt = f(t) for y(0)-1 if f(t) is the function whose graph is shown below 2 1 2 2-y+4y-u(t) for y(0)=y'(0)=0 3- y"+4y'+13y= e−2t sin3t for y(0)-1 and y'(0)=-2 17

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Write the given third order linear equation as an equivalent system of first order equations with initial values. Use Y1 = Y, Y2 = y', and y3 = y". - - √ (3t¹ + 3 − t³)y" — y" + (3t² + 3)y' + (3t — 3t¹) y = 1 − 3t² \y(3) = 1, y′(3) = −2, y″(3) = −3 (8) - (888) - with initial values Y = If you don't get this in 3 tries, you can get a hint.