#3. Solve the fallowing Caucly problem in R" x(0, 0) Uf-Ou t cu =0 on IR"x{t =0}. U = where c is a constant.

Q: Find dy/dx for each of the following cases a) x2 + 4.xy? = 0 b) x"y-a – P1x - p2y = 0 where p1, p2…

A: In question we have to find derivative of the given functions. Rules applied -

Q: Suppose u and v are differentiable functions of x. Use the given values of the functions and their…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Find y as a function of t if 16y" + 16y + 4y = 0, and y(1) = 2, y'(1) = 3. y =

A: The given differential equation  and the initial conditions .The objective is to find the solution…

Q: 2. Show that the function u = p(xy) + VTÝ v(y/x) provides the equation „Pu dx² 0. dy²

A:

Q: Question 7 The function f(r, y) = (4cy – 1)e" (A) has two stationary points (B) has a unique…

A:

Q: 3. Show that sinh a + sinh y = 2 sinh cosh %3D

A:

Q: What is the minimum value of y = 3 + cos 2x?

A: Please go through the attached solution. I hope that this solution will help you. Thankyou . Best…

Q: Determine óx' Determine óy' determine Tx'y'

A:

Q: 3) Is the function y(t)=cos(x(t)) linear or not?

A:

Q: 4 a. Consider the i.v.p x' = t^(2) + cos(x), x(0) = 0. Verify that the hypothesis of Cauchy Picard…

A:

Q: 2. 3y² dy/dx-1=3x²+6ydy/dx, y(0) -1 and determine the interval of x in which the solution is…

A: To solve the given initial value problem:  3y2dxdy​−1=3x2+6ydxdy​ with the initial condition y(0) =…

Q: The work done 'W' by a gas on a piston is given by P2 W = CP dp Where 'P' is pressure and 'C' is…

A: Given : Work done W = ∫p1p2 CP-1ndp Where P is pressure and C is constant.   To find : Show that…

Q: 1 Find the points of discontinuity of y = where и +и - 2 1 u = * - 1

A:

Q: Evaluate y = 4x 2 = [{(x² + 2y)dx + xy. dy} from 0(0, 0)to B(2, 4) along the curve

A: Given the integral is :                                  We have to evaluate the integral from…

Q: Is the equation separable, linear, bernoulli, or homogenous? dy а. dx x4 + 4xy² 2x3 + x²y +y³ b.…

A:

Q: Find extrenhum of one of the following function 1. 2(a, y) = sin2(x- 0.5) + artg (y- 0.5) rE (-1,1],…

A: Let us find the Extremum of the given function in the next steps.

Q: 32) Find ур(0) for the equetion y (4) - y" - 2y + 2y = 3xe³ + cos x

A:

Q: 12. Find frxyz for f (x, y, z) = sin (3x + yz)

A:

Q: Find the line integrals of F = 2yi + 4xj + zk from (0,0,0) to (1,1,1) over each of the following…

A:

Q: Show that y = x° + 3x +1 Satisfies y" + xy" – 2y' = 0.

A:

Q: 4. Find d²y/dx² for the following functions: a) y = sin x? cos 2x

A:

Q: y 4 Find Pr(3 < Y < 5), correct to four decimal places.

A: There are two types of variables: Continuous variables and discrete variables. Continuous variables…

Q: 11. Integrate the function. y? dy (49 – y²) 7y y + C V49 – y2 – sin y+C -1 - V49 - y2 | O A. O B.…

A:

Q: (ex + Iny + 1/) dx + ( 1/3 + (+In x + sin y) + Inxsin y dy = 0

A: