3. x = 1-5t and y -t+ 3 for 2 < t<6 %3D y (x,y) Domain:

Q: 20) Let y=7x+5x Then compute dy and Ay for X= -7 and dx =0.4. dy =? and Ay = ? Gounded 6o 4 decimal…

A: Derivative: - The derivative of the function is the equation that we find. The instantaneous rate of…

Q: Suppose f(0.25)=f(0.75)=b. If the Composite Trapezoidal rule with n=2 gives the value 4 for \int_0^1…

A: Introduction: The trapezoidal rule is a method to approximate a definite integral numerically. In…

Q: Solve the given optimization problem by using substitution. Minimize S = xy+xz + yz subject to xyz =…

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Q: Find dy and Ay for y = 3/x –1+ 2x at x = 2 with dr = Ar = 0.2.

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Q: Find the particular solution of y (9x - 2y) dx -x (6x - y) dy=0., when x=1, y=1. Let x=vy

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Q: (5* )csch x²+1 dy if Find dx 1. (a) y = x >0. (ecosh 5x) In Vx +1 )

A: Find your answer below

Q: Reducible to Homogenous method dy X-y-3 x-y-1 dx

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Q: ven f(x,y) = -2xy² where x = 5t and y = 8t2. Findf' (t) at t = 3. %3D

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Q: 2) Obtain the DE with respect to x of (x - h)² = 4(y-k).

A: Sol

Q: Z=8x+12y subject to 4x+6y>14 , 4x+5y > 9, x20, y20 x=? (2 decimal places) Minimize

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Q: d) s x sin sin (4x²) d x X Sin X-y=- / 7xーy=17 てる。4) Set Up only Area bounded between the lines…

A: Ans A:

Q: Verify that [(y- 2x \dx +(2xy +x*dy = [S -川- dA where C is the bounda ôy R defined by y = 0, x = 1,…

A: See the details solution in below

Q: The integrating factor of the DE   y(2x - y + 1) dx + x(3x - 4y + 3) dy = 0 is

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Q: obtain the particular solutions satisfying the indicated conditions: dx/y=(25-x^2)^-1/2dy; y(0)=1

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Q: Given the function f(x,y) cos 2xーx3eY +āyン COS find te second partial olerivative fxy.

A: Let f(x,y) is the given function.Then  fx is the derivative of f with respect to x taking y as a…

Q: 2. Find P.S. of when y (2x²-xy +y ²) dx − x²(2x-1) dy o y = 1/2. X = /

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Q: - Find dy at x = -1 if y=u³ +5u-4 and u = x² + x. dx

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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: · Use fourth-order Runge-Kutta Method to solve the following problem over the interval from x 0 to…

A: The given differential equation is,  dydx=y'=-3y+2e-x with an initial condition y0=2.  For…

Q: x³y³dy у2— 4у-21 (x – x4y)dy + (y + x³y²)dx :

A: See the solution and follow the step.

Q: Given that y' = 2x + x²y, where y(0) = -1 with step size h=0.1. Estimate the values of y(0.2) using…

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Q: If y In(z- y) then y at the point where y = 0 is equal to

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Q: Find the general and particular solution that satisfy the boundary condition. (3x + y)dx - (x +…

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Q: S S§y²cos(xy)dydx

A: we have given,                 ∫x =0x=1∫y=0y=π4y2cos(xy)dydx After arrangement,…

Q: 5. Find the particular solution (IVP) for the DE below: a) dx +2 =8x when x = 2, y = 6 b) 3y2 = 2x +…

A: Use variable separable method

Q: Obtain the solution using Integrating Factors Found by Formulas a.)  xydx − (x2 + 2y2)dy = 0

A: I am attaching image so that you understand each and every step.

Q: Eliminate the arbitrary constants y Iny = C,e "+ C, X-

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Q: 2e | 3జy S S dy da = Vsin(zy)

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Q: 2 3 2 Q5. Evaluate the value of integral |[xy'z dx dy dz . 0 11

A: I have stated the used formula in the solution

Q: Finf y' if x=Arccos(1-t), y=/2t-t2.

A: We can find the answer using chain rule as below.

Q: Use fourth-order Runge-Kutta Method to solve the following problem over the interval from x = 0 to…

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Q: 6 If the substitution y = xº is made, the 64 3√√y 3 + √√y integral [ 1 dy will become

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Q: Solve the general Solution of:  (xsiny/x- ycosy/xdx)dx + xcosy/x dy=0

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Q: Solve using the integrating factor by inspection  (2x²y - y²x + yx) dx + (3x³ - 4x²y + 3x²) dy = 0…

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Q: 2. Given the joint pdf of X and Y, fxx(x, y) = { '0" (4xy 0<x< y <1 other wise Find the marginal…

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Q: hich of the following is not variable separable? (А) 2ху dx + (х2 + 1) dy %3D0 A ye' dy - (e-y+…

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Q: Find dy at x = -1 if y = u’ +5u – 4 and u = x² +x . dx

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Q: Find L(y). / + 2x = 2 - x' = et (0) = x (0) = 0 -2 L (y) PL(y) = %3D s(s2 +2) 2s L (y) = %3D…

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Q: - Use Euler's method to estimate y(3) given y(0) = 1, and y' = x -. Use steps of h = 1

A: use euler method for finding the y(3)

Q: Let y(x) be the solution of the IVP dy - (y - 3)'dx = 0, y(0)=2. Evaluate y(13).

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Q: Find the general and particular solution that satisfy the boundary condition. (3x + y)dx – (x +…

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Q: Find the particular solution of y(9x-2y)dx - x(6x-y)dy= 0, when x=1, y=1. To start, let y=vx.

A: The given differential equation isyax-2ydx-x6y-ydy=0, with y1=1It can be written…

Q: find for x=1 the y value for partivular solutiom, (D^2+3D-10)y=0, when x=0, y=0 and x=2, y =1

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Q: 4x 28. If R = and errors in x, y, z be 0-001. Show that the maximum relative error at x = y = z = 1…

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Q: dy If y = f(x) is solution of dx? = 0 with the dy boundary conditions y = 5 at x = 0, and at x = 10,…

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Q: Q4) Find y" + 3y' 5y at x-5 where y = xsin(1/cscx))

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Q: #@3 g (x; y) = 7x3 - 49IXY + 7y3 Find and elassify all the extreema of the fine tion

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Q: Find dr dy at x = -1 if y =u° +5u – 4 and u = x² +x.

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Q: Obtain a family of solution 1. [x-y arctan(y/x)]dx + x arctan (y/x)dy = 0

A: Solution is given below: