iv) if zy = (x)- then zx +Zy =

Q: 2 dydx + f(x, y)dydx

A:

Q: Compute dy and ∆y for y = sqrt(x^3 + 1) for the change in x from x = 2 to x = 2.03. Is dy a good…

A: According to the given information, it is required to determine dy and Δ(y) for the given function…

Q: dt 34. tan t/4 – sin² t dy - Vy dy 35. 36. yV3 + (In y)? x² 1 38. dx 4х + 5 37. :dx /x² + 2x + 5…

A: 34) Solve the integration:

Q: Express a general solution to 2x(1 – x)y" + (3 – 10x)y' – 6y = 0 Using Gaussian hypergeometric…

A:

Q: (1+x²) uz + Uy = 0, u(1, y) = sec y

A:

Q: 3. Obtain the homogeneous linear equation satisfied by the following function. y = x² Sinx + e5x

A:

Q: Q4/ 1- Evaluate: f/2fy sinx dy dx ди 2- If u = x² + ey² ,x= sin 2t , y = cost² find at

A:

Q: Obtain the solution using Integrating Factors Found by Formulas y(y + 2x − 2)dx − 2(x + y)dy = 0

A: Find your answer below

Q: Show that if you differentiate both sides of x2 +2y³ = 6, the result is dy dx 2x + 6y² = 0. Then…

A: Given function is x2+2y3=6 Power rule of differentiation states that  ddxxn=nxn-1 And ddxconstant=0…

Q: Find Fxx and Fxyz of: XX хуz y2+Cos (xz) f (x, y, z) : 2 Siny

A:

Q: 0. dy for y = 4t dt. 4t +1 3x3 Use Leibniz's rule to find хр

A:

Q: Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8); fi-) U =

A: we can solve this as follows:

Q: 3 If y= Vx (x-1), find dy (Use rules, not a de finition XP

A: Given:         y=xx-1       dydx=ddxxx-1    Apply product rule:         ux·vx'=u'(x)·v(x)+u(x)·v'(x)…

Q: x°y" + 2x?y"+ xy'-y=0

A: A homogenous linear differential equation with variable coefficients given by,…

Q: obtain the particular solutions satisfying the indicated conditions: dx/y=(25-x^2)^-1/2dy; y(0)=1

A:

Q: (2y-x)(dy/dx) = 2x + y, given that y = 3 and  when x = 2 Homogeneous equations

A: Solve the following problem by substitution.

Q: Find aff dy dx² for f(x, y) = exy

A: I have done solution in detail....step by step....go through the solution

Q: What is fx , where f (x, y, z) = (sin yz)ez3−z−1√y ?

A: Given, f (x, y, z) = (sin yz)ez3−z−1y

Q: If the new DE is written in the form M(x, y) dx + N(x, y) dy = 0, one has My = || N, = X, Since M,…

A:

Q: Q1: If Z = x³ + y* + (x sin y) + (y cos x), Find Zx/Zy?

A: We are given: Z=x3+y4+(x sin y)+(y cos x)To find: ZxZy This can be calculated as follows:

Q: If f = 5xy2 - X³Y then find df at (1,1) dy %3D

A:

Q: Obtain the solution using Integrating Factors Found by Formulas a.)  xydx − (x2 + 2y2)dy = 0

A: I am attaching image so that you understand each and every step.

Q: Obtain the solution using Integrating Factors Found by Formulas. 2(2y2 + 5xy- 2y + 4)dx + x(2x +…

A: We can solve this using integrating factor

Q: Find dy/dr by differentiating implicitly if z +ry- 6r = 2.

A:

Q: 2f sen jz įdz -2 cos z + C 28. sen Jz dz = %3D

A:

Q: Finf y' if x=Arccos(1-t), y=/2t-t2.

A: We can find the answer using chain rule as below.

Q: dy 2. V16 + y²

A:

Q: Find the moment of inertia with respect to x-axis the aarea bounded by 2y^2-8y-16x=0 and the line…

A: The moment of inertia is the rotational analogue of mass. The expression for moment of inertia is…

Q: В. Find dz/əx , əz/əy at the point (1,1,1) if x³ + z² + ye*z + xz cos y = 0 .

A:

Q: 2 5. x = 1+t2 2 y= t(1+t?)

A:

Q: Solve the disfertial equation xy' -Y =Xtan ) %3D

A:

Q: dy of y=X Find

A: y = x^x Find dy/dx

Q: Show that 3x f(x, y) = (5x³ – 4y³)ey + 4xy? is homogeneous.

A:

Q: y = secx prove that d² y dx +y 2y

A: For y=sec x, we need to prove that d2ydx2+y=2y3. Here,            y''=secx''      =secxtanx'…

Q: 22. Find when t=, where x a(t + sint), y= a(I-cost) and a is a constant %3D

A:

Q: The approximation of I = f(x-3)** dx by composite Trapezoidal rule with n=4 is:

A:

Q: Find the par ticular solution of the differencial 4. given x=0 and y= eguation dy -20cH1) (x+1)

A:

Q: Express in form y=f(x) by eleminating the parameter x = ln t , y = 2 − t

A:

Q: dx Find the value ofat y=2 if x=z³+5z and z= dy (y² + 2y)'/³. -

A: Consider the function, x=z3+5z Differentiate 'x' with respect to 'z' as, dxdz=ddzz3+5z=ddzz3+5ddzz…

Q: 2. Show that the function u = p(xy) + Vxy v(y/x) provides the equation = 0. dy? -

A:

Q: cos y f(x, у, z) -D xz2 XZ

A:

Q: sech 2t dt Evaluate 3, coth 2t

A:

Q: If y= V (x-1), find dy (Use rules, not a de finition ) Xp

A:

Q: 3. Integrate! 12e-0.21 а) -dt b) 6r 3,2 Se041 dr dx c) f- x. V1+ In 3x?

A:

Q: (b)/ Use the Trapezoidal Rule with n = 4 to estimate ſ,(x3 + 1)dx.

A: To find: ∫-11x3 + 1dx using trapezoidal rule with n=4

Q: O fi[0,00)→R all continious Aunction aro Sx³f(x') dx = Sx f(x) abx %3D show this.

A:

Q: Solve for x = u + 1 and y = 2u² - 4u d²y dx² with respect to the parameter u

A:

Q: sec y Then y8 Let z dz dy y16

A:

Q: (b) If z = 9t²e 4t, find 4 dz dt

A: Given.