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Q: Find the supply function x = f(p) that satisfies the initial conditions. dx 10 x = 160 when p = $1…

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Q: (D²+1) y 4 see X . ニ

A: 1. We know, ∫secnxdx=n-2n-1∫secn-2xdx+secn-2xtanxn-1   Given differential equation,…

Q: y"– 2y' + 1 = (x + 1)e²x

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Q: ty (t+1)y + y = t²

A: Given That : ty"-(t+1)y'+y=t2 To find: solve the differential equation using determinant coefficient…

Q: (2) y" +y' + = (2t-a)simt Solve each of fhe felloving imitral valne problina : %3D

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Q: 2x Find the orthogonal trajectories of the family of curves y = Ce" .

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Q: Perform one iteration of the steepest ascent method to locate the minimum of f(x, y) = 4x + 2y +x? +…

A: given function fx,y=4x+2y+x2+2xy-3y2 with initial guesses x0=0,y0=0 claim- perform one interation of…

Q: Determine the orthogonal trajectories y-3x+1=ce 3x

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Q: Consider the following. Rx) = - 18x? 4 Ix4 - 18x2 %3D Find all relative extrema. (If an answer does…

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Q: Perform three iterations of the steepest ascent method to locate the maximum of f(x,y) = 3.5x + 2y +…

A: Consider the given function f(x,y)=3.5x+2y+x2-x4+2xy-y2 and initial guesses as  x=0y=0

Q: Q3) Use Euler's method to estimate y(0.02) ey-x y' 1+ e2y •y(0) = 2 (h=0.01) .What is the error in…

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Q: Determine the critical points of the function f(r, y) = 4x +4y + x²y+ xy? and whether they are local…

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Q: For y''+3y'+2y=e^-x, use the variation of parameters formula to find a particular solution. Show…

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Q: 6z dy (78)a

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Q: V Solve using variaton of parameters or recuction of order (D. 3D+ 2)y = (1+e*)

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Q: Solve using variation of parameters or reduction of order (D² – 3D + 2)y = (1+e²x)¯2

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Q: (a) For the solution that satisfies y(0) = 0, sketch the solution curve and estimate the following:…

A: (a) The solution curve with the direction field that satisfies the initial solution y0=0 is as…

Q: Use the explicit Euler method to plot the  estimate y(2) if y(t) is the solution to y' = t - y3 with…

A: Given IVP is y'=t-y3, y(0)=1 we have  f(t,y)=t-y3 Here using n=10 steps, Then step size h=upper…

Q: Q3. A parachutist weighing 192 lb falls from a plane (that is v, = 0). When the parachutist's speed…

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Q: Q3\ Solve the problem minimize * J[y]= [[v +y"- 2y dx ,subject to the conditions y (0) =1 and y(1) =…

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Q: An inner-city revitalization zone is a rectangle that is twice as long as it is wide. The width of…

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Q: Use the method of Variation of Parameters to solve. SHOW WORK. y" – y' – 2y = 2e-t

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Q: If a cannonball is shot directly upward with avelocity of 256 ft per second, its height above the…

A: Given: st=256t-16t2 We know that velocityvt and accelerationat is respectively first and second…

Q: 3. Find the family of oblique trajectories that intersect the family of the paraboles y =cx at angle…

A: given family of parabolas y2=cx at angle θ=60° claim- find the family of oblique trajectories that…

Q: Q3) Use Euler's method to estimate y(0.02) ey-x y' =- 1+e2y „y(0) = 3 (h=0.01) .What is the error in…

A: According to Euler's method: yn+1=yn+hf(xn,yn), where xn+1=xn+h and h is a considered step size.…

Q: The curved. surface of a rod of length (l) is against the flow of heat. If bot of ends of the rod…

A: Given heart equation is ∂2u∂x2=1c2∂u∂t Since c2=1 So heat equation will be ∂u∂t=∂2u∂x2…

Q: A parabola has the equation y^2 = -4ax. Determine the slope of the orthogonal trajectories. 2x/y O…

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Q: x' 5х + 2у y' — 20х — 5у ||

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Q: /A: Given; y? = 6kx %3D Find orthogonal Trajector.

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Q: 5) Find the linear approximation to estimate V9.247. Compare this to the true value and determine if…

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Q: Determine the largest interval in which the unique solution of (t-3)y +tant y = t, y(7)3D0 is…

A: The given differential equation is: (t-3)y'+ (tan t) y=t ;      y(π)=0

Q: Use the method of variation of parameters to solve the following y + 4y + 4y e- In z, z>0

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Q: Q3) Use Euler's method to estimate y(0.02) ey-x y' = 1+ e2y •Y(0) = 1 (h=0.01) .What is the error in…

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Q: Find the orthogonal trajectories of the given family of curves x^2 + y^2% D c^2. *

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Q: y" + y = sec (x)

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Q: Find the equation of orthogonal trajectories of the given function 8x² + y² = c.

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Q: A. y" – 2y + 1 = (x + 1)e²x

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Q: + 12du = 0, t> 0 with u(x, 0) = f(x), 0 < x < 1. Determine the characteristics and sketch them.…

A: Given: The given partial differential equation 3∂u∂t+t2∂u∂x=0 with  u(x,0)=f(x),0&lt;x&lt;1.

Q: Find the orthogonal trajectories of the family of curves y = ce^x. Select the correct response: x^2…

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Q: 4 + where f(1) = -2. y : dx 业

A: If (x, f(x)) is a point where f(x) reaches a relative maximum or minimum, and if the derivative of f…

Q: C = C(x) = (Hint: V = a²y) C' (x) = Solving C' = 0 yields that value of x that minimizes the cost.…

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Q: parameters

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Q: Find the critical points of the function f(r, y) = 8y3 +12x2 – 24ry and classify them as local…

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Q: SOLVE FOR THE ORTHOGONAL TRAJECTORIES X'(3k-x) - ky = xy

A: Take first derivative and eliminate k.

Q: C(x) = 1500 + 13x – 0.1x2 + 0.0005x3. - %3D Find the marginal inal cost finctien?

A: Given query is to find the marginal cost function.

Q: stimate the population will grow to P(t) (408)4, where t represents the number of %3D rding to this…

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Q: Find the orthogonal trajectories of the family of curves ey + 2x2 = k.

A: Given,  ey+2x2=k

Q: The maximm rate of change of the finction /(x.y,2) x In(yz) at (1:2;5 is equal to: V17/2 V17/4 O…

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Q: y" + y = sec (x)

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