f(x, y) = x4 + yA; x2 + y2 = 18

Q: xyz 3. If (x, y.2)= In +ef), find f,,f, and f.. 4

A: Given: fx,y,z=lnxyz4+e-3xy2z2 The objective is to find fx, fy and fz

Q: Find the solution of the DE using variation of Parameters y''' - 3y'' + 3y = (ex/x)

A: The given problem is to find the solution of differential equation using method of variation of…

Q: Find d2y/dx2 in terms of x and y. x2y2-10x=1

A:

Q: Find the general solution of y' = y secx

A:

Q: - f(x, y) = Vx5 + y5. Find f-(0, 0).

A: Given that fx,y=x5+y55.It is required to find fx0,0.

Q: Evaluate the integrals

A:

Q: Find DF of fcxiy)=x²e° at the point (-2,0)-

A: Given function is fx,y=x2ey. We have to find the ∇f at the point -2,0. We know that ∇f=∂f∂xi+∂f∂yj…

Q: 2. F(x, у) %3D — (у i-2x) y2

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

Q: Evalute fi f (y³ – xy)dydx -

A: NOTE: As per our guidelines, I have solved the first problem. If you want the answer of other,…

Q: b. min f (x, y) = 3x² – y² s.t. 2х — 4у 3D —11

A: Minimum value of function is determined using lagrange multiplier and its value is -33/4.

Q: rx dydx Vx2+y2 0.

A: We solve this double integration problem by substitution method as given below in solution

Q: 2 √2x-x² SJ J² J²^ √√√x² + y² + 2 00 y²)[2x − (x² + y²)]dydx -

A:

Q: Verify that ƒxy = ƒyx, for ƒ(x, y) = 2x3 + 3y2 + 1.

A: To verify that

Q: Find d²y if y =x² +3x-7 and x=2t+1. dt?

A: y=x2+3x-7 and x=2t+1

Q: dy * + 2(t + 1)y² = 0, _y(0) = - ip 1/8

A:

Q: Find ax dy x-2–1 given y = 2x3

A:

Q: find the general equation of : x^3dy+xydx=x^2dy+2ydx  ;y=e when x=2

A:

Q: use Separation of Variables to find the general solution. yy' = x

A:

Q: V1-y² -1 0 kpxpzp (,x + zA),I „«-,S

A: The given integral is: I=∫-11∫01-y2∫0x y2+x2 dz dx dy

Q: (3x)i + (3y)j + (3z)k F = x3 + y3 + z3

A:

Q: A Q2 Show that y=x+ is the solution of 3x – x = x+ y. dy dx

A:

Q: Solve using D-Operator 3. y + 2y + y = x²

A:

Q: Find the General and Particular solution of = 3y ; y= 3,when x = dx

A:

Q: q. r. √y² - 25 -dy, y > 5 y³ dx x²√√x²-1 2 ,x > 1

A: Solve both integral as following:-

Q: (b) Differentiate (Vx+ 1) with respect to x. 2/3

A: as per our guideline we can solve maximum one question you can repost other questions

Q: Find f2, fy, and f.- f(x, Y, z) = (4x² + 6y² + 3z²)¯05 fz = fy = f. =

A:

Q: d²y B Show whether y = Ax² + · x2 is a solution for x2- dy + x dx + 3y = 0 or not. dx2

A: If y=Ax2+Bx2 is a solution for x2d2ydx2+xdydx+3y=0...(1) then it satisfies equation (1).

Q: xyz 9. f(x, y, z) = x² + y2 + z2

A: Givenf(x,y,z)=xyzx2+y2+z2To find Domain of above functions

Q: 3 V9-y s S f(1,y)dxdy. y)dzdy. y-3

A:

Q: [v= -y +2x ,x' = 4y + x + t

A:

Q: f(x, y) = 6 – V4 - x2 - y2 is

A:

Q: Using the principles 2y. -3y + y = 5-3" Vn20 where y=1 and y₁=1

A:

Q: -V4-x² c3-x²-y² xdzdydx, 0. 0, J-5+x²+y²

A: We will find out the required value.

Q: f(x, y, z) = V9 - x² – y2 – z²

A: The given problem is to find the surface for the given function of three variables. Given function…

Q: Then: f(x, y) = exy 2z3y fxxy 2 2z?y fxxz' XXZ 2z y Ofxyy= x2 Of- 2z3y2 fx² X

A:

Q: F(x,y) = -41² - 2xy-4y² +z+y.

A: Follow the procedure given below.

Q: -3x2 F(x) = S*" t² dt %3D

A: TO EVALUATE THE FOLLOWING INTEGRAL F(x) ∫-x3x2 t2 dt FORMULA USED- ∫abxn dx = xn+1n+1 i.e substitue…

Q: Find X only using Crammers rule 2x+リ-「Z=D2 x2 -y +VZ 2 x? +2y +VN= 4

A:

Q: 29. t²y" - 4ty' +6y=0, t>0; y₁(t) = t²

A:

Q: Find Vy where = (x² + y² + z²) e¯¯ √√√x² + y² + z ²

A: Given :ψ=x2+y2+z2e-x2+y2+z2

Q: Vy² – 25 dy y3

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: f (x, y) = x² + 3y² + 4,

A: Supposing the question is asking to find the local minima value.

Q: Solve for y in terms of x and z. z = xy

A: A function defines a relationship between two sets, where one set is dependent on other set. Any…

Q: (x = s² – t² y = s·t³ z = 2x – 5y,

A: See the attachment

Q: f(x,y) = 3y3 – 2xy + 12y – 3x² – 8x – 16 then fy equals ух

A:

Q: 4. x = 9-y2 ,-2 <y S2 about y-axis vis

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.