SEPARATION OF VARIABLES 12.46. Solve each of the following boundary-value problems by the method of separation of variables. (d) du 22u at მx2 u₂(0, t) = 0, blom Ž u(2, t) = 0, u(x, 0) = 8 cos 37x 4 97x - 6 cos

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A: z=tan-1xy,  x=e2u+2v-2  &  y=vcosu Now when u=0 & v=1, x=e20+21-2  &  y=1·cos0⇒x=1…

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A: *By Bartleby policy I have to solve only first one as these are all unrelated problems.These are all…

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A: The solution to the given differential equations is explained below.

Q: 4. (4x 2+1)y'-y² 5. (y-1) dx-(x + 1) dy=0 6. (x²-1) dy + (y + 1) dx=0

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Q: 7. Given: y = 3 ; Find: dy/dt V16+tª -613 (16+t*) -2t3 (16+t*) (16+41) 글 (16+t*) ? (E) None of the…

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Q: Q6. Use the method of Variation of parameters to solve (i) y" +y : tan x.

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A: Integrating factor and solution of differential equation

Q: y" y = sin² x. -

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Q: 2. Used Euler's method to approximate y (0.5) and y (1) for the I.V.P y' = y + xe2x, y(0) = 1.

A: Given y'=y+xe2xand y0=1

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Q: Ex: FIND A COMPLETE SOLUTION OF EQ. y" + 3y" + 3y' + y = 0

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Q: Q.4 Use the one sided Greens function to solve the I.VP. -1 4t2y" +8ty' + y = 3t 2 Int2, y(1)=0,…

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Q: 9. Ut = 4uxx, (xo, to) = (5,4)

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Q: = 11. Obtain the solution using Integrating Factors Found by Inspection 1. ydx+2(y-x)dy = 0 2.…

A: 1. 2. 5.****Explanation:

Q: Salve for YsI The following initial value Salve for Y(s) The following prablem: y'- ay'+Y= coa…

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Q: . Is sin y x² dx + ydy = 0 a linear?  2. Is y' = y+x / x a homogeneous Equation?

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Q: IF x*y" + xy' +(x? - y=0 x>0 ,v,-x sinx , and y=Y,v. Which of the following 4. equations satisfied…

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