2. Use series approximation to Solve the Heat Equation Ихх — и, , 0 0 u(x, 0) = 0 < x < 1 1

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

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Q: Partial Solution of (4+ sin e) y'= e* (6 sec² e* - y cose"); y (ln π) = 1 T)

A: Particular solution

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Q: 4: A:Find the solution of the initial value problem (d^2 y)/(dx^2 )+5 dy/dx+6y=0□( ) y(0)=2, And…

A: Given A. d2ydx2+5dydx+6y=0  ;  y0=2 and dydx=0 B. 2yz-3lnz=2x+5y

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Q: two iterat x' = -2x+t, using successive approximation. x(0) = 1.

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Q: X X-2 such that (fog)(x) = X +2. Q₁/ let f(x) = , find a function y = g(x)

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Q: xy - 5y +6 2ху ху - 5у Option 4 Option 3 y? - 5 O Option 1 Option 2 Find dyldx at x = 1 y = tan(e* )…

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Q: 2. Evaluate aydA, where R = {(x, y) : 4 ≤ a² + y² ≤ 9, a ≤ 0, y ≥ 0}. x R

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Q: If the function f(x,y) is continuous near the point (a,b), then at least one solution of the…

A: It is given that dydx=y3 with y0=4. For the differential equation dydx=fx,y, if fx,y is continuous…