How do you solve the differential #dy/dx=(x4)/sqrt(x^28x+1)#?
# y = sqrt(x^28x+1) + C #
Is a First Order separable DE which we can sole by integrating:
Substituting into the RHS integral we get:
which is the General Solution
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To solve the differential equation ( \frac{{dy}}{{dx}} = \frac{{x  4}}{{\sqrt{{x^2  8x + 1}}}} ), you can use separation of variables.

Separate variables: ( \frac{{dy}}{{\sqrt{{y}}}} = \frac{{x  4}}{{\sqrt{{x^2  8x + 1}}}} , dx )

Integrate both sides: ( \int \frac{{dy}}{{\sqrt{{y}}}} = \int \frac{{x  4}}{{\sqrt{{x^2  8x + 1}}}} , dx )

Solve the integrals: ( 2\sqrt{{y}} = \int \frac{{x  4}}{{\sqrt{{x^2  8x + 1}}}} , dx )

Simplify and solve for ( y ).
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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