Using separation of variables solve the Laplace equation in 1< r < 2,0< 0 < π/2, subject to the boundary conditions au/ae (r, 0) = au/ae (r, π/2) = 0,1

Q: 7- y" + 4y = cos x, y (0) = 0, y(n) = 0

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Q: A particular solution of x²y" + xy' + (x? – 0.25)y = 3x3/2sinx, x>0, y,(x)=x-1/2sinx, y2(x)=x1/2…

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Q: 3. Use your solution from Part 2 to give solutions to the IVPS i. y" + 2y' + 16y = cos 3t, y(0) =…

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Q: y" +2y' = 3+ 4 sin(2t)

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Q: Find the general solution of the nonhomogeneous equation y4) + 2 y "+y=cos( 3 x) + 2 1 a) y =C,…

A: We will find out the required solution.

Q: 4 a. Consider the i.v.p x' = t^(2) + cos(x), x(0) = 0. Verify that the hypothesis of Cauchy Picard…

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Q: Solve nxx = ut in Rx (0, 0) with u (x, 0) = 5 cos (6x) + 7 sin (10x)

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Q: SHOW WHETHER THE FOLLOWING DE IS EXACT OR NOT 1. (y^2 – 2x)dx + (2xy + 1)dy = 0 2. x[1 – sin(y)]dy =…

A: As per bartleby guidelines, for more than one question only 1st one is to be answered. Please upload…

Q: What is the Euler equation associated with the Lagrangian L(x, y, y' , y") = 2x(y/")² – y²? O y+ 2y"…

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Q: ignments: Find a solution for the following equations in two different ways: analytically and…

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: 1. Find f(x, y) obeying = - sin(x)y and f(0, y) = }(y +2)². %3D %3D

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