3 years ago

Use the slope formula

Mathematics

1 answer:

larisa86 [58]3 years ago

6 0

Answer:

$m = -2$

Step-by-step explanation:

First lets fill in the variables

$m = \frac{3-9}{2--1}$

Now solve

3 - 9 = -6

2 - -1 = 3

-6/3 = -2

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The general solution of 2 y ln(x)y' = (y^2 + 4)/x is

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Replace $y'$ with $\dfrac{\mathrm dy}{\mathrm dx}$ to see that this ODE is separable:

$2y\ln x\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{y^2+4}x\implies\dfrac{2y}{y^2+4}\,\mathrm dy=\dfrac{\mathrm dx}{x\ln x}$

Integrate both sides; on the left, set $u=y^2+4$ so that $\mathrm du=2y\,\mathrm dy$ ; on the right, set $v=\ln x$ so that $\mathrm dv=\dfrac{\mathrm dx}x$ . Then

$\displaystyle\int\frac{2y}{y^2+4}\,\mathrm dy=\int\dfrac{\mathrm dx}{x\ln x}\iff\int\frac{\mathrm du}u=\int\dfrac{\mathrm dv}v$

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