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3 years ago

Factor the expression completely 8y-36

Mathematics

1 answer:

Shtirlitz [24]3 years ago

5 0

Answer:

4(2y - 9)

Step-by-step explanation:

$8y - 36 \\ = 4(2y - 9) \\$

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Let $v=x+y$ , so that $\dfrac{\mathrm dv}{\mathrm dx}-1=\dfrac{\mathrm dy}{\mathrm dx}$ :

$\dfrac{\mathrm dv}{\mathrm dx}=\cos v+1$

Now the ODE is separable, and we have

$\dfrac{\mathrm dv}{1+\cos v}=\mathrm dx$

Integrating both sides gives

$\displaystyle\int\frac{\mathrm dv}{1+\cos v}=\int\mathrm dx$

For the integral on the left, rewrite the integrand as

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Then

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and so

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Given that $y(0)=\dfrac\pi2$ , we find

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so that the particular solution to this IVP is

$\csc(x+y)-\cot(x+y)=x+1$

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