Use Laplace transforms to solve the following initial value problem. x''+x=sin 2t, x(0) = 0, x'(0) = 0 Click the icon to view the table of Laplace transforms. The solution is x(t) = ]]]. (Type an expression using t as the variable. Type an exact answer.)

Q: If m(v) =ln(sin^2(v)+1), find m'(v)

A:

Q: If f(z) = æ®sinh`1(6x) then f'(x) =

A: f(x)=x3sinh-1(6x)d dx(xn)=nxn-1d dx(sinh-1x)=11+x2d dx(a.b)=adbdx+bdadx

Q: If g(x) = sin(x) then g'(x) = g'(3 =

A: Use the definition of the derivative of a function.

Q: Given f''(x) = 25 sin(5x) and f'(0) = 3 and f(0) = 6. - Find f() = 6

A: Given that  f"(x) = - 25.sin(25x)......   (1) f'(0) = 3 f(0) = 6 To find  fπ6

Q: y''+y=(1)/(cos(x)) Solve

A: Consider the provided differential equation,

Q: f(x) = sin² x, find f'(x) Find f'(4) (round to 3 decimal places)

A:

Q: Find f'(x) = = 4-5 sin(x) cos²(x) f(x) = -4 sin(x) + 5 cos(x)

A: Given : f(x)=-4sin(x)+5cos(x)   To Find : f'(x)

Q: Suppose f''(x) - 30x – 160 sin(4x), f'(0) = 48, and f(0) - 10. Then f(x)

A:

Q: Suppose f"(x) = -16 sin(4x) andf'(0) = -4, and f(0) = 1. f(T/2) =

A:

Q: f'''(x)=cos(x),  f(0)=3, f'(0)=5,  f''(0)=5   find f

A: This problem can be solved by repeated integration. we know that integration will five us the…

Q: If f(x) = 4x(sin x + cos x), find f'(x) = f'(4) = -12 sin (4) + 20 cos (4) 0

A: given function