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kirill [66]
2 years ago
8

In order for you to answer the question correctly, please use the following image down below:

Mathematics
1 answer:
adell [148]2 years ago
7 0

Answer:

36

Step-by-step explanation:

24^2 = (12)(12+x)

576 = 144 + 12x

432 = 12x

36 = x

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Answer:

2.4003638e + 46

Step-by-step explanation:

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Licemer1 [7]

We're looking for a solution of the form F(x,y)=C. By the chain rule, this solution should have total differential

\mathrm dF=\dfrac{\partial F}{\partial x}\,\mathrm dx+\dfrac{\partial F}{\partial y}\,\mathrm dy=0

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The given ODE is exact, since

\dfrac{\partial(2xy^3+\cos x)}{\partial y}=6xy^2

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Then

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\dfrac{\partial F}{\partial y}=3x^2y^2-\sin y=3x^2y^2+\dfrac{\mathrm df}{\mathrm dy}

\dfrac{\mathrm df}{\mathrm dy}=-\sin y\implies f(y)=\cos y+C

\implies x^2y^3+\sin x+\cos y=C

With y(0)=\pi, we get

\cos\pi=C\implies C=-1

\implies\boxed{x^2y^3+\sin x+\cos y=-1}

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