Find constants C, such that u(x,y) = 2 C, sinh nx sinny is the solution of the problem: %3D ou du = 0, x,y € (0,), u(0, y) = 0, u(7, y) = 1, y e (0, 7m, u(x, 0) = 0, u(x, 1) = 0, xE (0, 7). Oa. 2 (-1)" nn sinhn Ob. T sinh(2n 7) Oc (1)"+1) 2 sinhn Od. (1--1)") 2 sinhn Oe. 1 1 nn sinh(2n7)

Q: x²y" +xy' – y = T

A:

Q: (t+ 9) y" + 2t y = 0 y(3) = 2n У 13) 2/3

A: We solve the given IVP  (t2+9)y"+2ty'=0.....(1) y(3)=2π,y'(3)=2/3

Q: f(7,y) = 8z² + 5y² + 4z'y+e7=y %3D Calculate 710

A: The given function is

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A: So, y=uvthen product rule is ddxuv=dudx×v+u×dvdx

Q: dy Find for y= csc (x)+ dx cos (x'+1). Do not simplify your answer. dy dx Given the equation x' + y'…

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Q: Werify that (x)=- 1-ce* dy Substitute (x) for y and find the derivative to substitute for dx…

A: We have to verify that  where c is an arbitrary constant is a one parameter family of solution to

Q: 3 5 The general solution for x'= 1 X is: %3D -1 21 +C2 a) x(1)=q,"e 1 1 +C2 1 b) x(1) = G -2t e 21…

A: