If r (t) = (cos(t), sin(t), 2) r(t) = (cos(t), sin(t), 2) , %3D T then fr (t) dt =

Q: 1. (e)(1-e²y)¹/² dx = dy 2. cos x cos y dy-sin x siny dx = x² cos x sin y dx

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Q: What is the integrating factor of the equation (2xy*ev + 2xy³ + y)dx + (x²y+ev – x²y² – 3x)dy = 0 A…

A: We have to choose the correct answer from the given option according to the given condition

Q: y(cos 2x)e*y – 2(sin 2x)e*y + 2x + [x(cos 2x)e*y – 3] = 0 %3D dx

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Q: 5. If the function y = y(x) is such that dy + 2y = x cos r, dr use the integrating-factor method to…

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Q: What is the integrating factor of the equation (2xy*e" + 2xy³ + y)dx + (x²y*e» – x²y² – 3x)dy = 0

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Q: The integrating factor of the linear DE dy - 8y = 5 cos x, dx is the function µ(x) = e-8z Select…

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Q: (dx — Зх — 2у dt dy 3D —х + 3у — 2z dt dz = -y + 3z dt %D (λ1, λ = 3, λ5)

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Q: Compute /. x² dx dy dz, where E = {(x, y, z) : x² + y² < 1,0 < z < 1}.

A: To evaluate ∬∫Ex2dxdydz, Where E is the region E=x,y,z:x2+y2≤1, 0≤z≤1.

Q: If y= sin f dt, then dy is dx 2x sin x sin x 2 VX sinx 2x sinx

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Q: What is the integrating factor of the D.E. 2y dx + (x- sin vy) dy =0 ?

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Q: Determine weather the statement is true of false. Explain your answer.

A: Given: ∫cos x dx = sin x+ c∫cos x dx = (sin x + π) + C To find: Whether the  statement true or false…

Q: (4, w/8) 1. (y cos xy dx + x cos xy dy) (0,0) (0,5) 2. e2* dx + ye2 dy) (5,0) (1,1) 3. 2(x dx +y dy)…

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Q: dx If x2 + y2 + z2 = 9, dt dy 6, and dt dz when (x, у, z) %3D (2, 2, 1). dt 3, find %D %3D dz dt II

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Q: f cos(mx) cos(nx) dx is equal to {A} [sin(m + n) + sin(m − n)] dx {B} [sin(m + n) - sin(m − n)] dx…

A: Let's find.

Q: If z = cos x - e¹, x = 1² + 1 and y = 5 + ln t, then equals: dz dt

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Q: If r = sin ( ƒ(t)), ƒ(0) = p/3, and ƒ'(0) = 4, then what is dr/dt at t = 0?

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Q: dw "(1),y = sin (1),-: 2) w=+ x= cos at =3 Ans. -1 dt

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Q: COS f(2, Y) af af dy f(x, y) = log, (3x) af %3D fe dy

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Q: If Y= e(sin x) dt apoint X = 2 then dy/dx

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Q: -cosh(x)dx 18) St?cos(2t)dt S 2y²e»*dy 19) Sxeax+1dx dx Sx²e2*dx 20) S x-x2 ) (2?/ª x)°e-In(x²)e3×dx…

A: We have to find the integration.

Q: (4,0,2) S sin y cos x dx + cos y sin x dy + 3 dz (1,0,0)

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Q: y = cos“ x, Find dy/dx O dy = - sin(x*) O dy = 4 cos3 x sin x dx O dy = - 4 cos x sin x dx O dy = -…

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Q: If x = y3 - y and dy/dt = 5, then what is dx/dt when y = 2?

A: Given,

Q: If the given linear DE is (y – cos² x)dx + cosxdy = 0, what is the integrating factor? |

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Q: find ƒx , ƒy  . 1.ƒ(x, y) = e^(xy) ln y 2. ƒ(x, y) = cos^2 (3x - y2 )

A: Hi! You have uploaded multiple questions. As per norms, we will be solving only the first question…

Q: 4) (у-сos' x) dx + cos xdy %3D0 5) 2y(y² - x)dy = dx

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Q: A ) Find ſ cos 5t dt dy B) If y = x² +; , x= 2t -5 then find dt

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Q: Find the general solution of (cos cos y +ycos x ) dx + (sin sin x – x sin sin y ) dy = 0

A: The given differential equation is incorrect and hence the correct differential equation is as…

Q: dw (C): If w = tan x and x = 4t³ + t ; Find ? dt dy

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Q: XZ 3) cos(x)-x²y + e + yz = 4, P (0,1,2)

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Q: dz az B. Find əx and ay 3. x eY+ cos xy36xz+5x²

A: partial derivative

Q: If Z = /xy + y, x= cos 0 , y= sin 0 when 0 = 2 dz By using chain rule find de

A: According to chain rule of differentiation .According to product rule of differentiation . According…

Q: 3. (sın 2y - 2x cos 2y) dx +( 2x cos 2y + 2xsın 2y)dy=Dd X = 2, Y = TT when

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Q: The

A: This is Linear Differential equation in x. We use method of separation of variables.

Q: If a = 5+ti and y = 3t - t then dy at t = 1 dz is :

A: as per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: What is the characteristic equation for dy 2. dt d²y y +2+e' sin 3t dt 2

A: Characteristic equation for the given differential equation:

Q: If X+y = x-y x2. -y2 and dx/dt = 12, then what is dy/dt when x = 1 and y = 0? О 12 O -12 12

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Q: If x = 2 sin* t and y = 3 cos* t, then find dy at t = %3D dx 4 а. 1.5 b. -2.5 с. -1.5 d. 2.5

A: Solution:

Q: If y = x2 and dx/dt = 3, then what is dy/dt when x = -1?

A: Differentiate both sides with respect to t.

Q: If f(x.v)= e-2x° cos(5x +y),- af dy O a. e-2[4xcos(5x +y) + sin(5x + y)] O b. -e-2x[4xycos(5x + y) +…

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Q: (sın 2y - 2x cos 2y) dx +( 2x coS 2y + 2xsın 2y)dy=d when x= 2, Y = T 3. COS %3D

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Q: * sin(Iny)dy is equal to y A -cos(ny) + C B none of these cos(Iny) + C y D cos((ny) + C cos(Iny) + C…

A: A standard integral in some cases can be converted to a standard integral with an appropriate…

Q: If x = 3 sin* t and y = 2 cos" t , then find dy at t = dx 4

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Q: Find the particular solution if dy/dt=sin(t) and y(2)=2.

A: Topic:- application of integration

Q: E(z, t) = ex cos(@t – kz + Þ1) + ey cos(wt – kz + $2) = €;E× +e,Ey %3D

A: Consider the given equation: Where,

Q: 4 cos x Let y = [, (2t + 1) (t + 8t)'/3 dt. Find dy/dx.

A: We will find out the required derivative for given function.

Q: Consider a disease that propagates according to the system dx 3 357 — Зху — Зх dt - dy = X dt х*у —…

A: Given that, dxdt=357-3xy-3xdydt=x2y-13xy-68y The equilibrium points are,…

Q: If r = sin (ƒ(t)), ƒ(0) = pai/3, and ƒ′(0) = 4, then what is dr/dt at t = 0

A: Given:

Q: If you have the equation dx/dt = a,are you allowed to multiply both sides by dt to change the…

A: We have given,

Q: dy dt 1 Find dx if 2y°t + t°y = 4 and d.x Cos t

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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.