a) If u=(x,7), where x = 0(1) and y=p(1), then that %3D prove du du dr ди dy dt Əx dt ây dt If x=rcose, y=rsin 0, then show that a'e 0. Əx

Q: 37. - dy y. dt

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Q: axy = with r, K, a, s, b>0. dt a) interpret what each term in the equation means, and…

A: Given: dxdt=rx(1-xk)-axy-----------(1)dydt=sy(1-ybx)------------(2)

Q: 2 f(t) = sint g(x, y, z)=x² + y² D(f) = D(g) = Dg= D (fog) (t) = D(f) D(g) = =

A: This is just directional derivative or simply gradient in several variable.

Q: (b)Find orthogonal trajectory of x'y = c.

A: The given problem is to find the orthogonal trajectories of x2y=c.

Q: at (x, y) = (1, 2) and z² = x² + y² if. dt = 9 and dy dt = 2.

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Q: OPnd w if ww=fcカっ) find メ= Sint dt

A: We have to find d2wdt2, Where w=f(x,y) and x=sint , y=t2 We will get  d2wdt2 by differentiating w…

Q: ƏF Find at (x, y) = (T, 1) if f (x,y) = cos vt dt. cos yt dt. ww

A: given,          fx,y=∫0x2ycostdt

Q: dy at x = 1 if y = 4x² + 1 and dt dx Find – 1. dt dy dt || ||

A: Solve the following derivative

Q: nd the indicated derivative. 8 dv 7) if v=t+- dt t

A: We are asked to find the derivatives.

Q: 8. Find dw/dt if w= xr^yz, x=t^3, y=1+t, z=1+2t

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Q: 3. Differentiate x²+1 () ± ([** 1 dt 4 1+ sin“ t d dx

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Q: Compute the differential dy  for  y=(6x+sinx)^3

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Q: Solve for x and y where dx/dt = x^2 + xy, dy/dt = y^2 + xy subject to condition x = 1, y = 2 at t =…

A: Non linear system of differential equations

Q: Find dy dx || dy dx x2 2 x2 for y=x | tant d dt 2 dt + (Type ex

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Q: dy / dx

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Q: 5) y = tanx secx 6) Y = b x+1

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Q: ди ди + 2х. -00 1, t- 1, a + 2x- dt dx и(х, 1) %3D f(x).

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Q: g Solve Rour of the following D.E A)(xュ)dx + 2xy dy dy B) ャリ=ex c) (xx v y'es )dx -(y- )dy zo D) (X…

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Q: Find dy dt dy dt at x = 3 if y = 5x² + 3 and dx dt 2.

A: Given:-y=5x2+3dxdt=2 at x=3To find : dydt

Q: If x² + y² + z² = 9, dz dt dx dt X dy = 4, and dt dz = 6, find dt when (x, y, z)= (2, 2, 1).

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Q: What does Cauchys EU theorem guarantee for The IVP:  dy/dt = -(y)^2/2t,  IC: (to,0)

A: Ft,y=-y22tDomain:{t,y∈R2:t≠0}∂F∂y=-ytDomain:{t,y∈R2:t≠0}∴function Ft,y is continous.So there exists…

Q: If z-f (x y): then its total differential can be expressed as * (),中 (). dyds dy + dz O Option 2 O…

A: