Use the Laplace transforms to solve the following initial value problem. x"+6x'+25x = 0; x(0)=2, x'(0)=5

Q: 16. F(m, r) = Gm/r² at (100, 10)

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

Q: Find the GS for x³y"" + 6x²y" + 4xy' — 4y = 1 − x − 2x² -

A: Solution:-

Q: Find f'(z) of f(z) = 3πi.

A: Compare the given function f(z) = 3πi. with f(z)=u(x,y)+i v(x,y) So,  u(x,y) =0 and v(x,y) = 3π

Q: Find the third derivative of y3= A 1/2 B -5/2 15 D -1 8

A:

Q: Find the differential of the following function: a) f(x) = x (2x³ + 9x)5 2t b) f(t) = (₁²₂)4 1-t2

A:

Q: Find the derivative of y with respect to x. y = cos1 (5x2 + 4) 10x + (5x2 + 4)2 -10x Vi- (5x2 + 4)?…

A: The given function is  y= cos-1(5x2+4)  We have to find the derivative of this function w.r.t. x

Q: If tan2(2y) – S cost dt = 4 - x² %3D dx

A:

Q: Which of the following sets are equal? (Select all that apply.) OA = {4, 5, 6} B = {xER| 3 <x< 7} O…

A:

Q: 53. df = (x+ 1)ye"dx + xe*dy

A:

Q: by s- differentiation find L(te-3t) = 1 .aO (s- 3) 1 .b O (s-3)2 (s+3) .dO (s+3) 2 1.

A: The solution is given as

Q: Find the derivative y = x + Vx + Vã 01+ + Ol+ + 1 1 + 쑤 None of these 3.

A:

Q: Find y" by implicit differentiation. x² + 9y2 と y"

A:

Q: Approximate f' (1) using the given data f(0) = 1, f(1) = 2, f(2) = 1, and f(3) = 10 and the Lagrange…

A: Lagrange inteerpolation is used to find a polynomial equation which passes through the given set of…

Q: Find the third derivative of y = (8x 1) solution and upload it on the designated field in jpeg or…

A: The given equation is y=8x-114to find the third derivative of the given function. Differentiation is…

Q: Compute the second derivative with respect to r of 3x + 8 y = at x = 1.

A:

Q: Find y as a function of t if 1296y" + 72y' + y = 0, y(0) = 4, y (0) = 7. y =

A: The given equation is second order homogeneous ODE has the form of ay’’ + by’ + cy = 0   The nature…

Q: 1. Find the derivative of the following by using the Theorem. a. y = In(3x3 – 6x +9) b. y = In[(2x –…

A:

Q: Compute the derivative of f(x) = (3x² – 1)1/4. %3D - O (6x – 1)!/4 a(322 – 1)5/4 O 3 2*(3x² – 1)-3,…

A: