se the method of Laplace transforms to solve the given initial value problem. Here, x' and y' denote differentiation with respect to t x(0) = - 3 y' = 4x+6y y(0) = 0 Click the icon to view information on Laplace transforms x(t) = y(t) = (Type exact answers in terms of e.)

Q: DETERMINE WHETHER THIS SERIES CONVERGES/ DIVERGES a) C 31)! IWE

A: Since you have asked multiple questions so as per our guidelines we will solve the first question…

Q: 16. F(m, r) = Gm/r² at (100, 10)

A: We wil use rules related to multi variable calculus to solve this.

Q: 4) Find the derivative of the function: x* cos x h(x) %3D Vx2 + 1

A: Answer

Q: d?y .if x = 212 – 3 & y = 3 – t* . dx² sing parametric differentiation, find

A: on solving this we get

Q: Find an equation of the tangent line to the graph of the equation at the given point. x² + x arctan…

A: The point on the curve through which tangent passes is, .The slope of the tangent is given by, The…

Q: b)Find the derivative of the function x cos (2x + 3y) = y sin x

A:

Q: Let y be a function of x and y' = dy/dx . By implicit differentiation, compute y′ from each of the…

A: Here we have to find the derivative. a) yx2-y2=3b) y2x+x2y=y

Q: b) Use implicit differentiation to find dy/dx of y² : X-1 x+1

A: Using implicit differentiation & quotient rule.