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

Q: solve the initial valve problem X'=AX, X (+₁) = x² Be sure to notice the intial time to G) A = ( ₁²…

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

Q: Find the differential and evaluate for the given x and d/x of the function, y = tan x, x = 0, dx =…

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Q: y' = tan y, y(ln 2) = F|N

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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…

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Q: x²y" — 5xy' + 8y = 8x6, y(z) = 0, 3 y 2 2

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Q: d sin x 1 dt| = dx et + 5 cO X 1 1 1 (A) esinx + 5 (B) e* + 5 (C) (esinx + 5) cos x (D) e sin x

A: We know that integration power rule is given as - Integration of xn is nxn-1.   Here i attached the…

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

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Q: In 5(x), the spike shifts to x = . It is the derivative of = shifted step U(x-1). The integral of…

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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…