x, prove that y¨= 2(y² +1)(3y² +1).

Q: 2 consider, Differentiate with respect to x', dy C」.2ス %3D de

A: From the image , two find a differential equation eliminating the constants from the given relation.…

Q: Let  f(x, y) = sin(15x2 + 3y2) Calculate the quadratic approximation of f at the point (0,0)

A: Given that,  fx, y=sin15x2+3y2 The quadratic approximation of the function fx, y at the point x0, y0…

Q: Find dY at x = -1ifY zu%5V=4 3. and u= X²+ X

A: Given that y=u3+5u-4 and u=x2+x We need to find dydx at x=-1 Take y=u3+5u-4 Substitute "u"…

Q: compute ∫_∂D(x^2ydx+xy^2dy, where D is described by 0≤x≤1, 0≤y≤x

A:

Q: Differentiate with respect to t. y = 7sin(x - t) -(7sin(x-t)) = dt

A:

Q: Let f(z) = 5z2 + 4z. Find u(x,y) if z = 8.17 + 3.6i. %3D Round off your final answer in five decimal…

A: Please find the attachment for the details solution

Q: dy Let y = (x2 – vx)4". Find using any method. dx -

A:

Q: Find fryz from the functions f(x, y, z) = 4x³y² – e²y* ++ 4y – x16 %3D - |

A: To find the third order partial derivative of the function fxyz f(x,y,z)=4x3y2-ezy4+z3x2+4y-x16

Q: Let y = x2 – 4.x. With x = 5 and Ax = 1, find the values of Ay and dy. %3D %3D -

A: y=x2-4x , x=5 and ∆x=1

Q: Verify Young's Theorem y? x2 z = In(2x + y) + +e(x+2y) y

A:

Q: Evaluate fSS 6e(²+y²+z²)/² dV over B where B= {(x, y, 2) : x² + y² + z² < 1}. Take T = 3.

A: Since we have    x2 + y2 + z2  expression in the integral and region B is the sphere of radius 1…

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

A:

Q: Find the total differential. w = (3x + 4y)/(y + 3z)

A:

Q: Q4) Find y" + 3y' 5y at x=5 where y = xsin(1/cscx))

A: Solution:-

Q: Q4) Find y" + 3y' 5y at x-5 where y = xsin(1/escx))

A: To find the y"+3y'×5y at x=5  Given y=xsin(1/cscx)

Q: Find the general solution for dø = z(z – z²)sec²Ø %3D | dz

A: the given differential equation is: dϕdz=zz-z2sec2ϕ we have to find the general solution of the…

Q: f(x, y) = In (x²y - x) %3D

A: Here, the given function is: f(x,y)=ln(x2y-x) First to find the first derivatives:…

Q: Find fx , fy and fz. 1 -1 f(x, y, z) = tan %3D \xy²z4, ().

A: Here we will find Fx,Fy,Fz;

Q: Find the quadratic approximation at (0,0) for f(x,y) = e^(x+y) * (xy-1).

A:

Q: 4. Suppose that z = x³y, x= t², and y = t³, find . dt = 12t11 dt 11t10 b) = 10t° dt d) = 9t® dt

A: This question is related to differentiation, We will solve it using given information.

Q: find given f (x, y) = eª + 2xy² – 4y at (0, 3) af dy'

A:

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

A:

Q: Find the I.F of 2y(x^2-y+x)dx+(x^2-2y)dy=0

A: Please see the answer below

Q: Calculate the LOS of y = x² LOS is x = a is b is c is

A: Given equation is in the form of ax^2+bx+c=y Here a=1 b=0 C=0.

Q: [-+] 5t dy 3.1는-51%3D-y dt

A: This is a linear 1st order differential equation.

Q: Consider the finction f(x,y) = x² + xy – 5x – y+ 1. Then:

A:

Q: Show that d/dz(z^2 z ̅) does not exist anywhere.

A: Here we show that ddzz2z does not exist anywhere.

Q: Calculate the LOS of y = x² + 2x + 8 LOS is x = a is b is cis

A:

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

A:

Q: (a) x² + zsen xyz = 0

A:

Q: Q) Compute for y(x) sec (2x) + 2x -1 and x(t) = 4cos(t) at t-1

A:

Q: - x'yt, show that fxy = fyx. 7,4 Given f(x, y) = et*

A: Given f(x,y) = e(x^4y^9) - x7y4

Q: Let f (x, y) = 2x³ + 4y³ + 19xy Find D = frx · fyy - fey at the point (2,2)

A:

Q: 2. In each exercise, obtain the particular of solution. a. xy dx + 2(x² + 2y²) dy = 0; when x = 0, y…

A:

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: Let ulx) be the solution of the IuP xy'-2y:x, yQ)=0 Evaluate y(32) %3D

A: In the question we have to find y(32).

Q: find for x=1 the y value for partivular solutiom, (D^2+3D-10)y=0, when x=0, y=0 and x=2, y =1

A:

Q: Suppose that f(x, y) = e 42? - ly + 7z + 2y then find the discriminant of f.

A:

Q: (ii)If y=(x+Jx* +1. prove that y'= Vx +1

A:

Q: What is the I.F of dy/dx=(y+y^2)/x?

A:

Q: Prove that (y – æ)(y + 3x)³ = cx° is a solution to 3x2 – 2xy + 3y² )dx = 4xydy.

A:

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

A:

Q: 3. For x= In /t y=t2, find y'-y"when x=0.

A: To find: The value of y'-y" when x=0 . Given: The value of function are x=ln(t) and y=t2. Formula…

Q: Given f(x, y) = - (4x°y + xy® ). Compute: dy?

A:

Q: Find f (1, 1) S(x, y) = In( %3D Vx² + y²

A:

Q: (b) If z = 9t²e 4t, find 4 dz dt

A: Given.

Q: 1 V1 – x z 1 – at x = 0 x, 2

A: Since you are asking part (c). We are answering only the (c) part for you.…