D = {(x, y) E R² :0

Q: dx 1s+ kıl35-x) +kaly-x) dy %3D dt k, , k. k3 are Con Stants.

A: Given system is dxdt=15+k135-x+k2y-xdydt=k2x-y+k335-y Here, 1k1=5⇒k1=151k2=10⇒k2=1101k3=5⇒k3=15 So,…

Q: A 3 cm length silver bar with a constant cross section area 1 cm (density 10 g/cm, thermal…

A:

Q: ds-(s + et)dt=0 (find DE,prove if exact or not)

A: dsdt=s+et  It can be solve by integrating factor method I.F =e∫1dt =et solution of DE is…

Q: Let y (t) be the solution of the initial value problem y"-4y +5y =e-2t 1 y (0) and y(0) = 17 %3D 17…

A: To find  The asymptotic behaviours as t tends to infinity.

Q: Q7 Show that CX,y) =e is Condinuous at co,0)

A: The given function is:  fx,y=e-x2+y2 The given point is 0,0

Q: A rectangular steel sheet is bounded by the axis x 0,y = 0,x = a and y b. The temperature along the…

A: pleas see the next step for solution

Q: Q2/ by using chain Rule to find dw at t = 1 if dt w = 2ye* – Inz ,x = In(t? + 1), y = tan 1t,z = et

A:

Q: b) Show that the “energy function" E(x, y) = 5 + is non-increasing along the solution, i.e., using…

A: (b) The objective is to show that the energy function  is non increasing along the solution, that…

Q: Let y(t) be the solution of dy/dt = 0.3y(2 − y) with y(0) = 1. Determine limt→∞ y(t) without solving…

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Q: The curved surface of a rod of length L is perfectly insulated against the flow of heat. The rod…

A: .

Q: You get to a step that you found a solution of the form: u(r,0) = > An(rn – r=")sin(n0), n=1 where…

A: In this question, we a general solution of Laplace equation is polar form is…

Q: A rectangular steel sheet is bounded by the axis x = 0, y = 0,x = a and y = b. The temperature along…

A: Solve the problem according to conditions

Q: 2s – 5t & y = 6s – 8t. %3D Let z(x, y) = x + 9y? where x = az дх ду да dy dz Calculate ds & and…

A: We use the chain rule

Q: 1. Show that the problem may be formulated in terms of the velocity potential o(r, 0) satisfying 6,…

A:

Q: Consider y = y on interval (-inf,+inf). y(0) = 3. The solution to this Initial Value Problem is OA.…

A: The general form of a  differential equation is dnydxn=fx,y,y',y'',....yn-1 . The initial value…

Q: HW 0 1f y=tanx show thats y" = -2Siny Cosy %3D

A:

Q: dz Use an appropriate form of the chain rule to find dt z = 8x"y³; x = t°, y = t Enter the answer in…

A: Topic :- Differentiation

Q: Let y' - 2y = 0, show that: i) y= e2x is a particular/exact solution %3D %3D %3De

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Q: Evaluate (2х — у) dx + (х + 3у) dy. C: elliptic path x = 4sin(t), y = 3cos(t), from (0, 3) to (4, 0)

A: Line integral

Q: A rectangular steel sheet is bounded by the axis -0y-0,x-a and y b. The temperature along the edge…

A: Steady state heat equation.

Q: dz at t = dt if z = f(x, y) = x² – 3xy+ 2y², x = x(t) = 3 sin 2t, y = y(t) = 4 cos 2t. Use chain…

A:

Q: 6. At time t, a particle moving in the xy – plane is at position (x(t), y(t)) where the x(t)and y(t)…

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Q: (a) Compute the average temperature of a wire in the shape of a helix c(t) = (cos(t), to, sin(t)), t…

A: To find- Compute the average temperature of the wire in the shape of a helix ct = cost, t10, sint, t…

Q: Q6) A string of infinite length is stretched from -o to +0 and subjected to the following initia…

A: Solve

Q: Find the approximate solution of the Poisson equation uxx + Uyy = -1 , Ix| s 1, lyl < 1 u = 0 at x =…

A:

Q: If x, y, and z are lengths of the edges of a rectangularbox, then the common length of the box’s…

A: Given- s=x2+y2+z2 To find- dsdt in terms of dydtand dzdt, if x is constant. Concept Used- As the…

Q: d²y z + y = e-2tsin(t) , y(0) = 0 and y (0) = 0 dt2

A:

Q: A rectangular steel sheet is bounded by the axis x = 0, y = 0, x = a and y = b. The temperature…

A: Answer is given below

Q: A rectangular steel sheet is bounded by the axis x = 0, y = 0,x = a and y = b. The temperature along…

A:

Q: Solve the boundary-value problem ди k dx? о 0 dt ди u(0, t) = 0, Əx 3D — h(u(1, t) — и), h > x=1

A: Given: To solve the given boundary- value problem, k∂2u∂x2=∂u∂t,       0&lt;x&lt;1,    t&gt;0

Q: d²s ds + dt 4t + 2cost where s = 0, ds/dt = 0, t= 0 dt2

A:

Q: The two functions x(t) and y(t) satisfy the simultaneous equations dx/dt - 2y = -sin(t), dy/dt + 2x…

A: Given: dx/dt - 2y = -sin(t), dy/dt + 2x = 5cos(t)

Q: Q6) A string of infinite length is stretched from -0 to +0 and subjected to the following initial…

A: Given vx=1-1≤x&lt;0-10≤x≤10otherwise

Q: e) Suppose that W= √√x² + y² + z², x= cos 0, y = sin 0, z = tan 0. dw T Use the chain rule to find…

A: According to our company's guidelines I can only answer (e), since (e) and (f) are not inter…

Q: Let z(x, y) = 2x2 3y2 where x = 2s – 4t & y = 9s + 8t. | dx dy ду az Calculate ds dz & and using the…

A: We have to find all first order partial derivatives.

Q: Minimize F(y, u) = f¿u²(t) dt under ý = -2y + u with y(0) = 1, y(1) = 0. Is your solution unique?

A:

Q: A spherical snowball of volume V cm³ and radius r cm dr = -5 cm/s. dt melts in such a way that -…

A:

Q: Assume that 0 < Po < M in equation dP 3D КP(М - Р), Р(0) — Ро. dt (a) Find the equilibrium points…

A:

Q: Find dy if y = In* +1 7 -t dy dt

A: Derivative is below

Q: Use the differential dy to approximate Ay whenx changes from x = -2 to x = -1.96. %3D y = x² + 1

A:

Q: a Z2=2+4i - [ (3 Im (2) + 2 Re (2)] dz Let e = 21=0 where C the parabola y = x² defined from z1 to…

A: Solution: (a) Let us consider C be a parabola y=x2 defined from z1=0 to z2=2+4i. Therefore, C can be…

Q: A rectangular steel sheet is bounded by the axis x = 0,y = 0,x = a and y = b. The temperature along…

A:

Q: Find a general solution to (x' +xy')y' = y implict form F(x, y)= C : Give an

A:

Q: E). f(x, y) = sen?(r2 – 0²) + In(r0 + 0), r = Vx2 + y² 0 = arctan con -

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Q: 24. Evaluate . (x – y) dx + (x + y) dy counterclockwise around the triangle with vertices (0, 0),…

A: Given integral is, It can be represented using Green's Theorem as,

Q: Q2) Use the chain Rule to find dw\dt of y w = =+2,x = cos²(t), y = sin² (t), z =, at t = 3

A: In this question,w is function of x,y,z and x,y,z are the function of t so first we find out…

Q: (も2-164 460) (7) 167 t60) dy dt =y y (8)- ) Flad as a Function of t rntenal ou what He solution and…

A:

Q: uct Theorem. 10. K y KM=

A: Solution

Q: Let (x² – x)ʻy" +y' -y=0,the D.E has regular singular point at x =

A: The DE x2-x2y''+y'-y=0. Then we have to find the regular singular points for the given DE.