1. f(x, y) = 1- x - y 2. f(x, y) = xy 3. f(x, y) = Vx² + y² 2

Q: 9. dy/dt = y²(y² - 1), -∞ < Yo <∞

A:

Q: 5- dy/dt = y²(y+1)(y-3), -∞<Yo<∞

A:

Q: 3. Find (6-+- vē)dt Vy 4. Find S- dy (4-yの?

A:

Q: Find the particular solution of y (9x - 2y) dx -x (6x - y) dy=0., when x=1, y=1. Let x=vy

A:

Q: Obtain the general solution of y√(1+x^2)dx+ x√(1+ y²)dy = 0 using variable separable method.

A: solution is given below..

Q: 16. Of all points (x, y, z) that satisfy 3x + 4y + 2z = 52, find the one that minimizes (x – 1)2 +…

A: Let f(x,y,z)=x−12+y−42+z−22   and    g(x,y,z)=3x+4y+2z−52≡0Apply Lagrange Multiplier method to find…

Q: Obtain the particular solution satisfying the initial condition indicated. (variable separable) dx…

A: Use the variable separable method and satisfy the initial condition. Also use the properties of…

Q: * = x- 2y+ 2z = -2x+y– 2z dt dy dt E = 2x – 2y+ z dt

A:

Q: Z=8x+12y subject to 4x+6y>14 , 4x+5y > 9, x20, y20 x=? (2 decimal places) Minimize

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: The integrating factor of the DE   y(2x - y + 1) dx + x(3x - 4y + 3) dy = 0 is

A:

Q: Suppose z = f(x,y) is a differentiable function of two variables. What do the partial derivatives,…

A:

Q: v² dx + x(xt y) dx = 0 LINE 1 let x= v2, dx = yda+ zdy y2 (ydz + zdv) + xz(vz +Y)dy= 0 vz (vdz t…

A:

Q: dy dy 6. = y³, y(0) = –2 dt 5. = y³, y(0) = 0 dt dy 7. dt = t(y² + 4), y(0) = 2 dy 8. dt 1+ y? y(0)…

A: Note: We will answer up to first 3 subparts. Please resubmit the question  which you would like to…

Q: x, y≥0 Corner points at ________________

A: The equations given are, 2x+4y≥8  4x+3y≥12  x, y≥0 To minimize , T=x+3y+10. First obtain the corner…

Q: Solve (x – y)dx + (3x + y)dy = 0 with the condition: y(2) = –1 O (2æ + 4y) – (2x + 4y) ln(2x + 4y) =…

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: 2.Find the particular solution of y (9x-2y) dx -x (6x-y) dy=0., when x=1, y=1. Let x=vy

A: Find out the particular solution.

Q: 36. Using the approximation dy dy h dr * Yn+1- y. and that dr 1, y = 2 when r 0. Then, y A h- 2 h+ 2…

A: Please see the answer below.

Q: dy 2х dx - y = 6e3t, dt dt dy 3x + dt dx - 3y = 6e3t; | dt x(0) = 3, У (0) 3 0.

A: Given, dxdt-2x-dydt-y=6e3t2dxdt-3x+dydt-3y=6e3t, x0=0, y0=0   We use the Laplace transforms…

Q: d² y dt² + 3 dy dt +2y(t) = 2e²¹ ; y(0)=0_

A:

Q: 6. If x = y3 - y and dy/dt = 5, then what is dx/dt when y = 2?

A: The given equation are x=y3-y,dydt=5  and y=2.

Q: 16. Let y = 4x² + 7x + 4. If Ax = 0.2 at x = 2, use linear approximation to estimate 4y Ay 2

A:

Q: 2e | 3జy S S dy da = Vsin(zy)

A:

Q: Integrate  zex^2 + y^2  over the cylinder  x2 + y2 ≤ 25, 2 ≤ z ≤ 5.

A: Integrate zex^2 + y^2 over the cylinder x2 + y2 ≤ 25, 2 ≤ z ≤ 5 as follows.Here, x2 + y2 = 25 and…

Q: 8. Find a continuous solution satisfying dy dr + 2xy = f(x) where = x if 0 < x < 1 0 if x ≥ 1 off…

A: Solve the following

Q: y' + 4y = e^(4t) %3D

A:

Q: Let y = v2x. Determine the point (x, y) that is closest to the point (5, 0). That is, deteremine the…

A: find the minimum distance from a point

Q: Find both first partial derivatives. z=(4 xy)/(x^2+y^2) fx(x,y)= fy(x,y)=

A:

Q: 23. (4y + 2t – 5) dt + (6y + 4t – 1) dy = 0, y(-1) = 2

A:

Q: 2-if (x - y) (x + y) = 1 prove that d²y + y dx² (2x)² = 1 dx

A: Topic:- application of derivatives    Note:- as per our guideline if more than one question uploaded…

Q: Find both first partial derivatives. f(x, y) = 8x – 7y + 10 fx(x, y) fy(x, y)

A:

Q: C(x, y, z) = 90 + 6x + 4y + z where x is the cost of 1 pound of one raw material, y is the cost of 1…

A:

Q: obtain the family of solutions [x − y arctan (y/x)]dx + x arctan (y/x) dy = 0

A: The detailed solution is given below Thank you

Q: Obtain the particular solution for: 2y" +2y=2sinx y(0)=0, y'(0) =1 By using method of variation…

A:

Q: (2) An integrating factor of (xy³ + y)dx + 2(x²y² + x +y*)dy = 0 is (a) y (b () (d) 2xy

A: We need to find an integrating factor of xy3+ydx+2x2y2+x+y4dy=0 Now, a differential equation of the…

Q: d*y 4)5t- dt + 3t () – (sin t)y = 0 dt 4 5)(sin x)y² + 2 y = 3x³ – 5 %3D 6) xy ? + 3 xy - 2 x³ y = 7

A:

Q: (1+x^3) dy-x^2ydx=0 satisfying the initial condition x=1, y=2

A:

Q: d²y 5 dy +6y= e7t dt dt2 y (0)=0 y'(0)=2

A:

Q: cos v f(x, у, 2) 3D xz2 af af 2 cos y Cosv siny df = - = - = - dx x2z2' dy dz xz3 XZ af cos v %3D af…

A: Topic:- partial derivatives

Q: 1 transforms the equation x dy + y = xy2sin(x) into The change of dependent variable y = dx dv A.…

A:

Q: d'y dy dy -+6 +11-+6y=4 dr dr dt y(0)= y'(0)= y'(0)= 0

A: Given the Ordinary differential equation:

Q: dy dy + 7 dt + 10y = e-t dt2

A:

Q: Minimize f(x,y,z) = x + 2y + 4z subject to the condition ** +y“ +z* = 7

A: Hello, thanks for your question .According to our policy I m doing the very first question . Please…

Q: 3. Find general Golution y" + y= Secx

A: Given that, find the general solution y''+y=sec3x (D2 +1)y=sec3x

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

A:

Q: Find the first partial derivatives of 3x – 2y f(x, y) = at the point (x, y) = (1,4). 3x + 2y af…

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: Find the differential dy. y =  x + 8 7x − 1

A: Assuming that y is given as: