x2+y2 Let fi (x, y) = In () = e ty a. Check whether fi(x,y) and f2(x,y) are homogeneous or not. (x²+y and f2(x,y) %3D x+y Je əx and x ay b. Find the value of x + y ax y ду

Q: Example: Calculate the value of (@w/0x) at the point (x, y, z) = (2, -1,1) if:- w = x2 + y2 + z? z3…

A:

Q: If z = f(u, v), u = g(r, s), v = h(r, t), r = j(s, t), and s= k(t) then dz dž=fu(u, v) [g- (r, s)[j.…

A: Given that we need to check that the statement for the derivative as given below is correct or not.…

Q: Find the antiderivative of the functions. S 6x dx S(12x - 5)dx S 3dx S(2x2 + 3)dx 1.) 2.) 3.) 4.)…

A: 1. ∫6x dx2. ∫12x-5dx3. ∫3 dx

Q: Saved DUndo 118% 1. Find mZJHI. KA+LB=G0° 3メ*2+12メー17=aoo (3х

A:

Q: Find V. (F x G), if F(x, y, z) = 16xi +j+8yk and G(x, y, z) = xi + yj - zk.

A:

Q: Find u · (v x w). (4, 4, 4) (4, 6, 0) w = (0, 0, 9) u = V =

A:

Q: дz State the multi-variable chain rule for du z=z(t, s), t=t(u, v, w), s=s(u, v, w) if

A:

Q: 20. Let (). ()- u = v = If æu + yv = w. (æ, y E R), then a - y = (A) 2/3 (В) —3/2 (C) 3/2 (D) –1/2…

A: To find the value of x-y from the given vectors.

Q: Differentiate: 3 a) F(y) = ( (y + 5y³) x²e* b) f (x) : x2+ex А c) f (x) : B+Cex

A:

Q: (a) Is Q (√6) ≤Q (√2 + √3) ? Justify your answer.

A:

Q: дz дz If z = f(x, y), find a and for the following equation əx ду z = x² + 3xy + y³

A:

Q: Vanessa invested $11,500 into a fund earning 7.50% compounded monthly. He plans to withdraw $650…

A: 1) Total fund will be available after 5 years Just before first annuity withdrawal :   Amonut = P *…

Q: Eliminate the Arbitrary Constant(s): 1. y = c,x2 + C2xe* 2. Iny = c, + C2x

A:

Q: Find V x (V × F) if F(x, y, z) = 9xyj+ 5xyz k. V x (V × F)

A: Given function is F→x,y,z=9xyj^+5xyzk^. To find:  ∇×∇×F→ Concept: Cross product formula for given…

Q: Find V x F for F(x, y, z)= - -xZ + y² i+ -yz x² + y² =j+√x² + y²k.

A:

Q: 3.a) Eliminate the Arbitrary Constants in the equation: y = C1sin(2x + C2) y" + 4y = 0 у' — 4у%3D0 O…

A:

Q: 3. Find V x F for F(x, y, z)= -x2 i + x² + y² -yz x² + y² =j+√x² + y²k.

A: Given function:To find Known facts:

Q: A) B) dx₁ dt dx₂ dt dx₁ dt dx2 dt dx₁ dt dx₂ Wh = x₁ + 2x₂ + 2x₁.x2 = x₁ + x₂-X1X2 is stable or…

A: Given :           A) dx1dt=x1+2x2+2x1x2    dx2dt=-x1+x2-2x1x2           B) dx1dt=-x1+x2+x12…

Q: 6. Consider the sequence defined by the recursive formula an = 10 - a,-1 with ao = 2 (a) What are…

A:

Q: Soly

A: Given  u = ( -1 , 0, 1, 1)   v = ( 2, 3, -1, 0)

Q: af Let f(x, y) = x³y + 8. Compute (1, 2) and -(1, 2). ax ду

A: Given: fx,y=x3y+8

Q: of find 4x + 9y of and dy For the function f(x,y) = %3D of dx ||

A: We can answer this question as below

Q: If z varies direct to the square of y and y varies inverse to x (x,y,x) = (20,120,100) Then find the…

A: z varies directly to the square of y, so z=my2 y varies inversely to x, so, y=nx Therefore,…

Q: 4y² Given the function f(x,y)= +e*y _find each of the following. SIMPLIFY

A: Given function is, fx,y=4y2x3+ex2y To find fxy(x,y) Find fxx,y partially differentiating the given…

Q: дz Find and əx дz ду' yz + x ln y = z²

A: Given query is to find indicated partial derivatives.

Q: Let f(x, y) = x³ + y³ + 3x²y + xy + y². Find fæ, fy, fax, fry, fyy.

A: The given function is,

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.