Q: substitute derivation equation and derivation equation 2, in equation 3 ? [Me] =C(1– x)– p[Me,L,] 1 (L]=Cx-q[Me,L,J P[L]<[Me] dx +9[Mc]d[L] dx 0.

Q: 7- cos y dx + (x siny - cos²y)dy = 0

A: Note: as per guidelines we support one question in one request . kindly repost next question in next…

Q: Solve dy dx =-y with y(0) = 1. Find y(0-01), y(0-02) by Runge-Kutta method.

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Q: Using S- dx x√√x-1 Rationalizing Sfy)dy, find ffy)dy Substitution

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Q: Q3\ using Euler method, find an approximate value of y corresponding to x€ [0 -0.7], Given = x(x +…

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Q: 4x + 5 6 - Evaluate the integral dx. V3 – a? a)5 arcsin V3x + 4/3 – a2 + C b)5 arcsin V3x – 4/3 – x2…

A: =?

Q: (test for exactness) (2ysinxcosx - y + 2y²e*v¨ )dx = (x - sin'x - 4xyev" )dy %3D

A: Given DE is 2ysinxcosx-y+2y2exy2dx=x-sin2x-4xyexy2dy Test the exactness of the given DE.

Q: Determine whether the equilibrium at x = 0 is stable, unstable, or semi-stable. dx 4x² - x³ dt 3 The…

A: We need to find the equilibrium at x=0 is stable, unstable, or semi stable. given,…

Q: The order and degree of the differential d³y V dy equation: 7+ i. - dx3 dx 3, 2 7,3, 3, 1 3, 7

A: The order of a differential equation is the highest order of the derivative that is present in that…

Q: 2. Integrate numerically the given function, fx0.1(1.2-x)(1-e20(x-1)) dx with the multiple-segment…

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Q: lim r.y)→(0,0) (4 + (x² + y²) In(x² + y?)) Dose not exist -00 00 1 4-

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Q: Q) Use the chain rule to express dy / dx in terms of x and y for the :following y =1-! 1 t = 1-x and…

A: Consider: y=1-1t and t=11-x. Calculate dydxin terms of x,y at x=2. Calculate dydt and dtdx using…

Q: dx using miscellaneous substitution will yield to secx + 1 nsforming - S 1+2 / dz √²-22² dz 1+z²…

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Q: Finding a General Solution Using Separation of Variables. dy/dx= (x-1)/y3

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Q: Use the differential dy to approximate Ay when x changes from x = -3 tox = -2.99. y = x2 + 1 Enter…

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Q: Using the autonomous equation dy/dx=f(y), how it is possible to obtain information about the…

A: Image is attached with detailed solution.

Q: A particle moves along the x-axis. Its acceleration is a = -t2. At t = 0, the particle is at the…

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Q: I-x² f (x, y, 2) dz dy dx 1-x² Jo

A: we have to find the region of integration

Q: 2. Find the General Solutioh oG (əx -3y-2) dx-Cx-2y) dy =0

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Q: 2х- 1 dy for y = dx J (*-7) (1* -7) dt. Use Leibniz's rule to find dy dx

A: Given, y=∫02x-1t4-7dt Using Leibniz's rule we have to find dydx. According to Leibniz's rule we…

Q: 2 4) d?y |1+ () dx2 dx, Find the: Туре: Order: Linearity: Why?: Unknown Function: Independent…

A: Topic:- differential equations

Q: Assuming 8x³ - 10y² - 2xy = 0 defines y as a differentiable function of x, use the theorem dx dy dx…

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Q: Test for exactness (2ysinxcosx - y + 2y?ey )dx = (x - sin?x - 4xye*y )dy %3D solve exact de,…

A: First we have to check exactness then we solve the differential equation.

Q: 8. Find the length of the curve y = e on the interval 0, ln 2| %3D

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Q: dx Using Rationalizing Substitution S- -=Sf(y)dy, find ff(y)dy- X√√x-1

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Q: Using the Chain Rule Find dy/dx for y = (x2 + 1)3

A: Given, y=x2+13 We can write given function as, y=x2+12x2+1 Now by using the chain rule,

Q: 17. Using Runge-Kutta method of fourth order, solve dy y2-x2 dx y2 + x2 | with y(0) = 1, at x = 02…

A: Numerical methods: Ruge-kutta method

Q: The linearization of ex at x = 0 Derive the linear approximation ex = 1 + x at x = 0.

A: Given, ex ,x=0 We know that, The formula for the linearization is, Lx=fa+x-af'a

Q: exact diffential equation of (y+2xy³)dx+(1+3x²y²+x)dy=0

A: We have to solve the exact differential equation: y+2xy3dx+1+3x2y2+xdy=0 Rewriting the equation, we…

Q: +(g-1)dx -t +(2xy-Siny]dy=o

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Q: Solve the disfertial equation xy' -Y =Xtan ) %3D

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Q: Find the differential dy when x = 1 and dx = 0.2 Find the differential dy when x = 1 and dæ = 0.4

A: Answer

Q: Q1\ Use Runge-Kutta method with (h=D0.1) to solve the equation y+ 3xy - 6y = 0 ; given that yo = 1…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Q2. Solve y [xcos (e)- + ysin (:)] dx – x [ysin 2) – xcos (2)] dy =

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Q: Integrating Factor by Formulas: (4) (4xy + 3y² – x)dx + x(x + 2y)dy = 0 (5) y(x + y + 1)dx + x(x +…

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Q: Test for exactness (2ysinxcosx - y + 2y?e*y )dx = (x - sin?x - 4xyey")dy %3D solve exact de,…

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Q: ;+ 2リ+y = ハ- cos(t) Slove the D- E t2 with. Ze Vo initial cuudition s En gineer ing Analysis

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Q: Let Fes) = fcx-s)dx Find fes) for %3D fex).x^, a constant the funchion where n is

A: Definite integral of the function ∫abf(x)=F(b)-F(a) where F is antiderivative of f .

Q: II ACTIVITY # 8: esinx dx use N=5 SOLVE USING TRAPEZOIDAL AND SIMPSON'S RULE

A: For trapezoidal rule  h = b-anh = π-05h = π5 x 0 π5 2π5 3π5 4π5 π esin x esin 0 = 1 esinπ5 ≅…

Q: 2 Approximate 0.5źdx using trapezoidal rule. X-4 Select one: a. -0.02678571 b. -0.2276571 C.…

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Q: Solve using separation of variables xy^2 dx + e^x dy = 0; when x -> infinite, y -> 1/2.

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Q: Solve = 1 +y, y(0) = 0 by Picard's method. %3D dx

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Q: A point is moving along the graph of the function y=1/8x^2 +3 such that dx/dt = 3 cm/sec. Find dy/dt…

A: NOTE: Refresh your page if you can't see any equations. . take the derivative with respect to t

Q: approximation of I = [" f(x)dx using composite Simpson's rule with n=4 is:

A: In this question, we evaluate the definite integral by using the composite Simpson's rule for n=4.

Q: y2 Use the modified Euler Method to solve the ODE = dx subject to y = 1 when x = 0 1+x on the…

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Q: (2xsinycosy - x+2x²evx´ )dy =(y-sin?y -4xyex )dx

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Q: Find the differential dy of the given function. Y= square root 7- x^2 Dy=

A: To find the differential dy of the given function

Q: 3y(x2 - 1)dx+(x +8y–3x)dy= 0 when x= 0, y=1 |

A: Given: 3y(x2 −1)dx+(x3 +8y−3x)dy= 0 when x= 0, y=1