Let y (z) be the solution of the initial value problem 4) - " + 2y/ + 2y = 0 y (0) =a, y (0)-B, y" (0) = 1, and y" (0) = -1 What are the values of a and B if lim y (r) = 0? O AI a=1 and 3-1 a=0 and 8 -1 a=1 and 3--1 a--1 and 3=0 and 1

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Q: Problem 2.3 i. and 2.3 ii

A: Given initial problems are

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A: Given initial value problem can be evaluated as shown below by using substitution method

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Q: Solve the initial value problem. 4 y(x) = 4 sec(3.x) tan(3.x) ; y(7) = %3D 3

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Q: Solve the initial- value problem:

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Q: Example 10: Form the partial differential equation by eliminating the arbitrary constan a and b…

A: We can find the answer as below

Q: Example 12 : Form the partial differential equation by eliminating the arbitrary function from z= xy…

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Q: Consider the initial value problem * = (tan (z + y))² y (0) = 0 %3D What is limg-1 y (x)?

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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.