# How do you find the general solution to #dy/dx=2yx+yx^2#?

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To find the general solution to the differential equation ( \frac{dy}{dx} = 2yx + yx^2 ), we can use separation of variables. First, we'll rewrite the equation as:

[ \frac{dy}{dx} = y(2x + x^2) ]

Next, we'll separate the variables by dividing both sides by ( y(2x + x^2) ):

[ \frac{1}{y} , dy = (2x + x^2) , dx ]

Now, we integrate both sides:

[ \int \frac{1}{y} , dy = \int (2x + x^2) , dx ]

[ \ln|y| = x^2 + x^3/3 + C ]

Where ( C ) is the constant of integration. Finally, we'll exponentiate both sides to solve for ( y ):

[ y = e^{x^2 + x^3/3 + C} ]

This is the general solution to the differential equation ( \frac{dy}{dx} = 2yx + yx^2 ).

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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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