# Explain why both y = x-3 and y = x+2 can both be considered solutions to the differential equation dy/dx - 1 = 0?

See below.

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An alternative approach is to work backwards from the Differential Equation and provide the General Solution.

We have:

This is a First Order separable DE, and we can write in the form:

And "separating the variables" gives us:

Integrating we get the General Solution :

Are both solutions, as is for example:

Given an initial condition we can provide a value for the Arbitrary constant and supply a unique solution or a Particular Solution .

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- What is a solution to the differential equation #dy/dx=e^-x/y#?
- How to you find the general solution of #dy/dx=3x^3#?
- What is a general solution to the differential equation #y'=2+2x^2+y+x^2y#?
- How do you use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by #y = 1/x^4#, y = 0, x = 1, x = 4 revolved about the x=-4?
- How to you find the general solution of #4yy'-3e^x=0#?

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