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Differential equations

I need to know how to find a particular solutions to an initial conditions. i know how to find the explicit solution of a differential equation but cannot remember how to find particular solutions. please show your working to help me understand. thanks

Problems (also attached):

Given the attached information:

1) So how do I find the corresponding particular solution that satisfies the initial condition y = 1 when x = 0. ?

2) What is the value of y given by this particular solution when x = 7? Give your answer to two decimal places. (Note that your calculator should be in radian mode for this calculation) why??

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Solution Summary

This solution is comprised of a detailed explanation to answer how do I find the corresponding particular solution that satisfies the initial condition y = 1 when x = 0 and what is the value of y given by this particular solution when x = 7.

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