For geotrophic flows in the atmosphere of the Earth, the following first order system of ODE is formulated. X' = AX where 1 0 0 X2 and x= A = 1 X4 The solution vector X relates to the velocities and accelerations of two perpendicular components of airflows tangential to the surface of the Earth. The symbols u and a represent the kinematic viscosity of air and the Coriolis constant; and both of them can be assumed as constants. (i) Find the eigenvalues of the matrix;

Q: Given h(x) = (-x² – 2x – 2), find h' (0)-

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Q: Find the derivative. r = 20 - 04 cos 0 dr = 40° cos e - oª sin 0 OP dr = 403 sin e - 0ª cos 0 de O…

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Q: x f(x) g(x) T(X) g'(x) 3 1 9 9 6 7 4 3 3 2 -5 g(x+f(x)), x=3

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Q: Differentiation. Find the value of the derivative of (iz + 6z2)° at 4i.

A: Let us define function f as                             f(z)= iz3+6z23

Q: by s- differentiation find L(te-3t) = 1 .aO (s- 3) 1 .b O (s-3)2 (s+3) .dO (s+3) 2 1.

A: The solution is given as

Q: Let X1, X2, X3 and X4 be a random sample from population with pdf 0 < x < 1 X, fx(x) = 0, otherwise.…

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Q: Find the solution of the following linear ODE given that y(5)=3 dy Зу = (x – 4)² х—4 dx

A: Use integrating factor for the differential equation.

Q: Write down the auxiliary (characteristic) equation and then find a general solution of the given…

A: Hiven differential equations are (a)  and (b) .We need to find the auxiliary equation and then…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.