Find the Jacobian a(x, y) / a(u, v) for the indicated change of variables. x = eu sin v, y = eu cos v a(x, y) _ a(u, v)

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A: This is a problem related to differential equation. Please follow the procedure given below.

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A: Solution ) we have option 3rd  y"+ 4y = 0 Auxilliary equation  m2 + 4 = 0 m2 = -4 m = √( -4 )  m =…

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A: We use the method of langrange multipliers to solve the given problem.

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Q: Find the general solution of the given higher-order differential equation. y"" - 8y" - 9y' = 0 y(x)…

A: The given differential equation is y'''-8y''-9y'=0 ............ (1)  Equation (1) can be rewritten…

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Q: ¡ (ew - 3) dw? O ew - 3w+C O - ew + 3W + C O -ew - 3W + C O ew - 3+ C

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A: The given differential equation is d3ydx35-7xd2ydx23+5dydx=11ey

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Q: Find the Jacobian (x, y) / d(u, v) for the indicated change of variables. x=u-v², y = u + v a(x, y)…

A: Follow the procedure given below.

Q: Sketch the region R of integration and switch the order of integration. 81-x2 LV²²- -10 O -10 f(x,…

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Q: R. -6 -2 7 π/2 ett 4 2 i -2 2 π/2 4 ett 2 4 O 2 4 T/2 8 6 4 2 π/2 4 2 D 2 2 P 50 4 8

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Q: =S • I = dx (x²+9²)² 2 ans ? tr 493

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A: To find the equation for the function.

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Q: Tutorial Exercise Find the domain of the function. 7 |x²-161 g(x) = Step 1 The domain is the set of…

A: To solve the given domain problem of the functions.

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A: We will solve.

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Q: Find the domain of the function. 7 |x²-161 g(x)

A: Domain : It is the set of all real numbers for which the equation is defined.

Q: Find a formula for the inverse of the function. \\ f(x) = f-¹(x) = 1+e 1-e

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Q: Find the general solution of the given second-order differential equation. 3y"+y' = 0 y(x) = =

A: To find out the general solution of the given differential equation.

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A: Given the sum is 714+2 + 724+2 + … + 784+2

Q: Find the Jacobian a(x, y, z) a(u, v, w) for the indicated change of variables. If x = f(u, v, w), y…

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Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

A: Given solution is y=C1+C2x+C3e4x