If F(x)= J. x) = [", "+!dt then F'(x) dt , then F'(x)= /3 sint

Q: if f(x)=2x-cos(x), Use Newton's method to approximate x, starting from the initial value xo=0

A: Solution:-    fX=2x-cosX           x0=0    f'x=2+sinxwe know      x1=x0-fx0f'x0           =0-f0f'0…

Q: integrate t2 sin(2t) dt from 0 to 8pi

A: We will  Integrate by parts using the formula:              ∫u v dx = u∫v dx −∫u' (∫v dx) dx.

Q: Can i get help step by step please

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Q: Classify the differential equation as separable or linear (1+2*); dy = 4y dx

A: To classify the differential equation as linear or separable.

Q: By separating variables, find the general solution of the differential equation dvc = - dt RC' where…

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Q: A more detailed version of Theorem 1 says that, if the function f(x, y) is continuous near the point…

A: Explanation- Given that, The initial value problem is- ydydx=x-1;  y0=1 By simplifying it further,…

Q: y' – y = 2te',

A: Laplace transform: L(y'(t))=py(p)-y(0) L(y(t))=y(p) L(2tet)=2(p-1)2

Q: A more detailed version of Theorem 1 says that, if the function f(x, y) is continuous near the point…

A: Explanation-  Given that, The initial value problem is- dydx=x2-y2 ; y0=1 Here, The function is-…

Q: Find the general solution of the differential equation with the help of lablace transform

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Q: If f(x) = A B (C) tanx S 0 sec ³x 1+e tanx 1+tan²x 1+ e tanx 1+12 sec²x 1+e tanx In (coor) 1+ e'…

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Q: Use integration to find a general solution of the differential equation                  dy / dx =…

A: The given equation is  dy / dx = tan2 x

Q: D. Solve the differential equation using Loaplace transform of y" + y = 6sin 2t ; when y(0) = 3 and…

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Q: 5. x- + Px = sin t %3D dt

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Q: Find dy/dt when x = 1 if y = x2 + 7x - 5 and dx/dt = 1/3.

A: Given:

Q: What is an integrating factor of the nonexact DE  (2y^2 + 3x) dx + xydy = 0 ?

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Q: 1. Find the total differential of the ff. at (1, -2).

A: The given function is f(x,y)=xy2-3y+2

Q: By using Laplace transform to solve y" + y = e with y (0) y (0) = y" (0) = 0, what would be Laplace…

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Q: Show that cos x is the integrating factor of the linear differential equation dy/dx= sec x+y tan x

A: Integrating factors are useful for solving ordinary differential equation  that can be expressed in…

Q: A more detailed version of Theorem 1 says that, if the function f(x, y) is continuous near the point…

A: The given initial value problem is ;    ydydx = x-1  with  y(1) = 0 We have to determine the…

Q: If In/x² + y? =sec, use implicit differential to proof the following: - (x²+y²). sec, tan dx

A: The given function is: lnx2+y2=secyx

Q: gin (t) et dt

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Q: Find the total differential w = x2yz2 + sin yz

A: Partially differentiate w = x2yz2 + sin yz with respect to x and keep y and z as constants.…

Q: By applying Newton's second law to a body at a certain distance x at time t, the following…

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Q: Suppose that every constant multiple of a solution is also a solution for a first-order differential…

A: It is given that the differential equation dydt=ft,y, where ft,y is continuous on ty plane. Suppose…

Q: Suppose y = square root 2x + 1 where x and y function of t . A) if dx/dt =12 , find dy/dt. When x= 4…

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Q: Let xy = 3 and dy/dt = 4. Find dx/dt when x=2?

A: Given :                xy = 3  , dydt = 4 To find :                      dxdt when x=2

Q: What is the differential equation of the orthogonal trajectories of the family of curves y = Cx ? (A…

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Q: A particle, initially at rest, moves along the x-axis such that its acceleration at time t > 0 is…

A: Given acceleration, a(t)=cost,       t>0 And v(0)=0, x(0)=3

Q: Classify the given differential equation according to its type, order, degree, and linearity. du…

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Q: x²y' + 2xy = In x, У(1) 3D 2

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Q: 5) If y = x³ + 2.x and dx/dt = 5, find dy/dt when x = 2.

A: Q.5) If y=x3+2x and dxdt=5 Find: dydt when x=2

Q: Find dy/dt at x = 1 and y = x^2 + 3 if dx/dt =

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Q: at x sin- 1 lim e J1 x→1 In x " 2 dt =?

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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: Show that the sine integral satisfiesthe (differential) equation xS'(x) + 2S''(x) + xS'''(x) = 0.

A: Given information: Sx=∫0xsinttdt To prove xS'x+2S"x+xS'''x=0

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Q: Find the general solution of the differential equation and check the result by differentiation.…

A: On simplification, we get Now integrating on both sides, we get

Q: Suppose 4x + 9y - 25, where x and y are functions of t. (a) If dy/dt-, find dx/dt when x = 2 and y =…

A: Given: 4x2+9y2=25 Since, x and y are functions of t, therefore differentiating each sides with…

Q: Consider the nonhomogeneous differential equa 1 "(x) + y(x) = e '+ sin a

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Q: A population x of rats satisfies the DE dx /dt ka?. Initially there are x(0) = 2 rats, and their…

A: The general solution of a differential equation always contains a constant of integration. The…

Q: Find dy dy dt at x = z - 1 if y = -5x² + 3 and dx dt 5.

A: topic:- derivatives

Q: dt What is the linearization of h(x)= 6+ at x=1? cos (1 -1)

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Q: b) Find if e Vt2 +5 dt + siny = x- xcosy rsinx ycscx

A: According to Leibniz' rule:

Q: What is the slope field of a differential equation y' = ƒ(x, y)? What can we learn from such fields?

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Q: find the general solution of the differentialequation and check the result by differentiation.dy/ dt…

A: The given differential equation: dydt=x32 Integrate both sides of the differential equation with…

Q: If x3 + y3 = 9 and dx/dt = -3, then what is dy/dt when x = 1 and y = 2?

A: Given,

Q: Find at x = -2 if y = - 4x² + 3 and dy dt dy dt = dx dt - 1.

A: Topic = Derivative As per guidelines , at a time only one question can be answered. pleas repost for…

Q: Let x > 0 and b > 0. Show that

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Q: Can i get help step by step please

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