Q.3 (a) Express j= 3yî + x²j – x²k in terms of cylindrical coordinates. %3D - (b) Transform g = 2f from spherical polar coordinates to cartesian. %3D

Q: onsider the initial-value problem y" +4y 5 sin 3t, y(0) = 0, y/(0) = 3. y'(0) = 3. %3D %3D olace…

A: In this question, the concept of Laplace Transform is applied. Laplace Transform The Laplace…

Q: How to solve this equation y''' - 8y" + 4y' +48= 4x2+1 using Laplace Transformation.

A: Converting the equation in Laplace transform:…

Q: find the Laplace transforms A preliminary in- of the functions in Problem. tegration by parts may be…

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Q: 4) Find the critical points of the parametric equations x = t* - 1 y = t3 - t

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Q: Find the general solution of the DE s

A: Given: - The differential equation is, dydx=2yx+x3y+xtanyx2 To find: - The general solution of the…

Q: Which boundary conditions of the Sturm-Liouville problem y" + iy 0, 0 < x < 1 determine the…

A: Given,         f(x)=∑n=1∞bnsin(πnx)

Q: 4–x2 Sở SY dy dx using polar Evaluate 2x-x2 Coordinates.

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Q: 12/2 Use polar coordinates to evaluate dydx. 3 0. (x² + y²)²

A: To convert cartesian coordinates to polar coordinates , put x=rcosθ, y=rsinθ , dydx=rdrdθ So,…

Q: 5. Eliminate the parameter to find a Cartesian equation of the following curves. et (a) x = vt+1, y…

A: Eliminate parameter t.

Q: Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below. y" -…

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Q: 2. Compute [²√x by first changing it to polar coordinates. 1 -√3x (x² + y²) ² dy dx

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Q: 5. Eliminate the parameter to find the equation of the ellips Sx(t) = 4 cos(t) + 1 ly(t) = 3 sin(t)…

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Q: find the Laplace transforms A preliminary in- of the functions in Problem. tegration by parts may be…

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Q: Given the IVP: y" - 4 y' +4 y = 6, y(0) =0, y'(0) = 3 %3D A) Use the Laplace transform to find Y(s).…

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Q: 4. (i) Use the parametric equations of an ellipse, x = a cos (t) , y = b sin (t), 0 < t 2m, to find…

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Q: 9/Find Parametric equations for the Line that is tangent to the curve r(t) = eti + (Sint); + In…

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Q: find the Laplace transforms A preliminary in- of the functions in Problem. tegration by parts may be…

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Q: find the Laplace transforms A preliminary in- of the functions in Problem. tegration by parts may be…

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Q: find the Laplace transforms A preliminary in- of the functions in Problem. tegration by parts may be…

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Q: 25. Find the general solution of the equation dy = 2y + 2e-. dt (This equation is linear, but please…

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Q: 9/Find Parametric equations for the Line that is tangent to the curve r(t) = eti + (Sint)j + In…

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Q: 6) roțațion 90° counterclockwise about the origin Made with Infi nite G eometrv

A: topic - rotations

Q: 3. Consider the parametric equations x = 1+ cos(t), y = -2+ sin(t), 0sts2M. 3.1. Find an equation…

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Q: 8. Find the positive constant a(> 0) so that the parametric x = at, y = -t? is a solution to y =…

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Q: Solve Laplace Equation in the circular domain 0 srs 1, with Dirichlet boundary condition, u(1,0) =…

A: Given, the Laplace equation                           urr+1rur+1r2uθθ=0             (1)in circular…

Q: 4) Find the critical points of the parametric equations x = t* – 1 y = t3 -t

A: Topic:- application of derivatives

Q: 3) i.- Given the IVP: y" +3y-4y = 20, y(0) = 0, y (0) = -5. %3D %3D | A) Use the Laplace transform…

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Q: TY 7. Compute dy dx by converting to polar coordinates. V4-2 x2 + y2

A: 7. Given integral is ∫02∫-4-x20xyx2+y2dydx The objective is to solve the integral using polar…

Q: 1. Prove that a. a L{sin at} = a²+s² b. Find Laplace transforms of the followings i. sin 3t + e2t…

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Q: 1.5 3-X Evaluate the integral *dy dx using polar coordinate

A: Follow the procedure given below.

Q: Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below.…

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Q: *+ xx + x = 0 has a centre at the origin. %3D

A: Given: x.. +xx.+x3=0

Q: find the Laplace transforms A preliminary in- of the functions in Problem. tegration by parts may be…

A: Given:

Q: D. Multiple Choice 1. Given: [(4x + 3)²D² - 12(4x + 3)Dx + 64]y = 16[(4x + 3)² sec² (In|4x + 3)],…

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Q: 2y )dx - (x +3 cos y)dy around the parallelogram havi - 6

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Q: 4. Solve for the critical points of the given parametric equation: x = t³ – 1; y = t² + t

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Q: find the Laplace transforms A preliminary in- of the functions in Problem. tegration by parts may be…

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Q: Example 10.26. Using Picard's method, find approximate values of y and z corre- sponding to x = 0.1,…

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Q: 4) Find the critical points of the parametric equations x = 5 – In t y = t + Int

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Q: 1. Sketch the direction field and solution curve for the given DE and condition. Sketch the…

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Q: (a) Solve : 2. at given that : u (0, t) = 0 u (5, 4) = 0 u (x, 0) = sin (xx) using Laplace…

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Q: Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below. y'' -…

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Q: A uniformly stretched string and fastened to two points 10 meters apart. The displacement of the…

A: This question is about application of Euler's equation

Q: HW 5 Find the laplace transforma tion of the Pollowsng 3x' +34 + 5X = 25 Cost X(0) = 2 2x`- 33 5…

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Q: Sole the IVP using the method of laplace transforms.   w''-10w'+25w=25t+140   w(-2)=1   w'(-2)=-12

A: According to the given information it is required to solve the initial value problem using laplace…

Q: 8. Solve for the critical points of the parametric equations x = t - 1,y = t² +t

A: To find the critical points of parametric curve x(t)=t2-1, y(t)=t2+t

Q: 1. (a) Consider the equation e'un+2ayury +2e"u- sin(y) u =0, where a is a real constant. Determine…

A: We will use basic knowledge of PDEs to solve this question.

Q: 3. Find the exact length of the parametric curve x = sin-1t, y = In /1 – t2, 0<t<

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Q: a. Find the solution set for log, 2+2.log3 x= log, (7x-3) b. Plot the polar curve r 2(1-cose) in…

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Q: Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below. y" -…

A: Given that y''-6y'+9y=cos 6t - sin 6ty0= 2; y'0 = 6 Using laplace and inverse laplace, solve the…