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nlexa [21]
3 years ago
5

Verify that the indicated function y = ϕ(x) is an explicit solution of the given first-order differential equation. y' = 2xy2; y

= 1/(16 − x2)
Mathematics
1 answer:
Andre45 [30]3 years ago
4 0

Answer with Step-by-step explanation:

We are given that a differential equation

y'=2xy^2 and y=\frac{1}{16-x^2}=(16-x^2)^{-1}

We have to verify that the function y=\phi(x) is an explicit function of the given first order differential equation.

Differentiate w.r.t x

y'=-(16-x^2)^{-2}(-2x)

By using the formula

\frac{dx^n}{dx}=nx^{n-1}

y'=\frac{2x}{(16-x^2)^2}

Substitute the value of y in given differential equation

y'=2x\times (\frac{1}{16-x^2})^2

y'=\frac{2x}{(16-x^2)^2}

LHS=RHS

Hence, the function y is an explicit function of the given first order differential equation.

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