# What is the general solution of the differential equation? : # dy/dx = x+2y #

The General Solution is:

# y = -1/2x -1/4 + Ce^(2x) #

We can use an integrating factor when we have a First Order Linear non-homogeneous Ordinary Differential Equation of the form;

We have:

Which we can write as:

This has transformed our initial ODE into a Separable ODE, so we can now "separate the variables" to get::

We can proceed via an application of integration by Parts

Then plugging into the IBP formula:

We have:

Using this result, we can write the DE Solution as :

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The general solution to the differential equation dy/dx = x + 2y is y = Ce^(2x) - 0.5x - 0.5, where C is an arbitrary constant.

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The general solution of the given differential equation dy/dx = x + 2y is y(x) = Ce^(2x) - (1/2)x - (1/4), where C is an arbitrary constant.

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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.

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