(b) Use the method of complementary functions and particular solutions, to determine the general solution of: d'x dx 3 dt2 - 4x = 2 e-t dt dx When t = 0, x 0 and = -5. dt

Q: dy Find - by implicit differentiation. Jx + y +Vxy =4 dx

A: Given: x + y + xy = 4

Q: Differentiate the function y = In (3x² – 6x + 7). Choose the correct setup below to start differe d…

A:

Q: '5 f(x) = -9 evaluate the following. J2 2 Given f(x) dx = 3 and (a) f(x) dx (b) f(x) dx '3 (c) f(x)…

A: Given : ∫02fxdx = 3 and ∫25fxdx = -9   To find : (a)∫05fxdx (b)∫52fxdx (c)∫33fxdx (d)∫25-8fxdx

Q: A balloon leaks air (changes in volume) at a rate of one-third the volume per minute. Write an…

A: Given : A balloon leaks air (changes in volume) at a rate of one-third the volume per minute.

Q: Find an implicit general solution for the ODE dy/dx = [2(2y−x)] / (x+y)

A:

Q: Find the derivative of y = 3x² − 2x + dy = 6x 2 dx dy dx dy dx Oy = = 3x - 1 = 3x - 2 6x - 2

A: Given query is to find the derivative of the function.

Q: If y=x^(2)+81, find the relationship between (dy)/(dt) and (dx)/(dt) Where x,y depend upon t.

A: We have to find the relationship between  and where  and  depend upon .We use Chain Rule to answer…

Q: By using appropiate substitution, solve dy hpT i. x2 dx 1 = xy – y² ii. – 2. (2х + у)е2»+у | dx

A: Consider the provided question, (b) (i)

Q: Find the derivative of the function y = (4x + 5)°(5x + 1)~ª. dy dx II

A: For the solution of the problem follow the next step.

Q: Find the derivative of the function x3 y = / 9vi sin(?) dt. %3D

A:

Q: 4. coth(ln x)

A: