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Bernoulli Substitution
For:
$$\frac{dy}{dx}+P(x)y=Q(x)y^n$$
put:
$$v=y^{1-n}$$
Then:
$$\frac{dv}{dx}=(1-n)y^{-n}\frac{dy}{dx}$$
Usage
- Converts the Bernoulli equation into a linear equation in $$v$$.
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Bernoulli Substitution
For:
$$\frac{dy}{dx}+P(x)y=Q(x)y^n$$
put:
$$v=y^{1-n}$$
Then:
$$\frac{dv}{dx}=(1-n)y^{-n}\frac{dy}{dx}$$
Usage
- Converts the Bernoulli equation into a linear equation in $$v$$.
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