3 years ago

So The final step in any equation is this

Mathematics

1 answer:

lara31 [8.8K]3 years ago

7 0

Isolate the variable

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

Sav [38]

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

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

$\implies\ln|u|=\ln|v|+C$

$\implies\ln(y^2+4)=\ln|\ln x|+C$

$\implies y^2+4=e^{\ln|\ln x|+C}$

$\implies y^2=C|\ln x|-4$

$\implies y=\pm\sqrt{C|\ln x|-4}$

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3 years ago

Megan has a bag of beads. She uses 28 beads to make each necklace. She makes 12 necklaces. Megan has 135 beads left over.

Bezzdna [24]

If you are asking for how many beads she used in total for the 12 necklaces it is
336. If you are asking how many beads she had before making the necklaces it is 471. If you are asking how many necklaces can she make with the leftover beads it is about 4. Hope this helps plz mark a crown.

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3 years ago

I need help on this and the person who answer this correctly gets a BRANLIST(answer if you know)

denpristay [2]

Answer:

14.425

Step-by-step explanation:

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At the hardware store, you purchased a box of nails for 17 dollar. You had a coupon that took off 20% from the nails. Sales tax

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