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Calculus - Differential Equations - Vectors - Circle Equati

Question (1)
First find a general solution of the differential equation dy/dx=3y. Then find a particular solution that satisfies the initial condition that y(1) = 4

Question (2)
Solve the initial value problem dy/dx=y^3 , y(0) = 1

Question (3)
Find the centre and radius of the circle described in the equation
2x2 + 2y2 - 6x + 2y = 3

Question (4)
Given a = 2 i + 3 j , b = 3 i + 5 j , and c = 8 i + 11 j express c in the form ra + sb where r and s are scalars

Question (5)
Given a = < 4 , - 3 , - 1 > and b = < 1 , 4 , 6 > find a × b

For detailed description of the questions in mathematical font and format, please see the attached question file.
Thank you

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Solution (1)
The general solution is y = c e3x
The Particular solution is y = 0.199148 e3x

NOTE: For detailed step by step solutions of all these question, please see the attached solution file.

Solution (2)
First we find the general solution ...

Solution Summary

Solution to the posted problems is given with step by step instructions so that the student could easily understand and use these solutions as model solutions to solve other similar problems.

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