Consider the following initial-value problem. y" - 3y' = 8e²t - 2e-t, y(0) = 1, y'(0) = −1 Find L{f(t)}, for f(t) = 8e²t - 2e-t. (Write your answer as a function of s.) 6s + 12 L(f(t)) = (s-2) (s+1) Use the Laplace transform to solve the given initial-value problem. y(t) = 8e²t - 2e

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Q: x² – 9 Let f (x) -. Find and simplify f' (x) and f"(x). %3D Ax2 + B f'(x) = where A = |-4 B = 54 C =…

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A: NOTE: Refresh your page if you can't see any equations. . here we have

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Q: P(t)=12t 4 -6f +=+7 .3 y 3 (x³ +2x +7) (4–x²

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Q: h(x) = px³ + 4px + 1, where p and q are constants. Given that h(-1)=-41 and h'(-1)=67, find the…

A: h( x ) = px3 + 4px + qxh( -1 ) = -41 h'( -1 ) = 67

Q: 7.If f(x)= 2x – 1 and g(x)= x² – 2x, find f(3)/g(2). -

A: Given fx=2x-1 and gx=x2-2x. To find: f3g2 Solution: Finding f3.  f3=2·3-1=6-1=5 Now, finding g2.…