Bernoulli Differential Equations

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Last updated 5:42 PM on 7/10/26
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Bernoulli Differential Equation Form

A Bernoulli differential equation is nearly identical to a linear, first-order differential equation; however, the only exception is that the forcing function is now multiplied by a factor of y^n, where n is a real number higher than 1.

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Process of Solving Bernoulli Differential Equations

We must first divide by y^n to obtain a simplified version of the equation; from there, we then do a substitution such that v = y^(1-n) whereby v is the middle term. From there, we then differentiate v with respect to v and plug in all of the necessary components.

<p>We must first divide by y^n to obtain a simplified version of the equation; from there, we then do a substitution such that v = y^(1-n) whereby v is the middle term. From there, we then differentiate v with respect to v and plug in all of the necessary components. </p>
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Reduction

Once we have plugged all of the variables in for v, we then treat the equation as a first-order, linear differential equation and identify the integrating factor and solve as necessary.

<p>Once we have plugged all of the variables in for v, we then treat the equation as a first-order, linear differential equation and identify the integrating factor and solve as necessary. </p>
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