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Hi all, hope you all had a great Christmas,

I had a difficulty with theses two problems,

1. Show that y=1/x + x/2 is a solution of the differential equation,

dy/dx=1-y/x, where y=1.5 and x=2

2. Solve the differential equation, dy/dx=e^4x-y, where y=1 and x=1/4

In your final answer express y in terms of x.

For question 1 my understanding is that I should differentiate the y= function and then sub that in for dy/dx and they should equal with some algebra. My problem is when do you input the values for x and y?

For question 2 I think its a separable equation that you would separate, integrate to solve then sub in the x and y values to find the constant of integration. My issue is how to separate, I've tried to take the natural log of both sides? But im really lost

Thanks so much in advance!

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# Homework Help: Basic First ODE and Separation problem

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