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SOVA2 [1]
3 years ago
6

Find the roots of the following equations: x-1/X=3,X is not equal to zero.​

Mathematics
1 answer:
lana [24]3 years ago
5 0

Step-by-step explanation:

X-1/X=3

X-1=3×X

X-1=3X

-3X+X=1

-2X=1

X=1/2 Answer

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Consider the differential equation <img src="https://tex.z-dn.net/?f=%20x%5E%7B2%7D%20%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D6%20y%5E%7
Nutka1998 [239]
As a Bernoulli equation:

x^2\dfrac{\mathrm dy}{\mathrm dx}=6y^2+6xy\iff x^2y^{-2}\dfrac{\mathrm dy}{\mathrm dx}-6xy^{-1}=6

Let z=y^{-1}\implies\dfrac{\mathrm dz}{\mathrm dx}=-y^{-2}\dfrac{\mathrm dy}{\mathrm dx}. The ODE becomes

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y=\dfrac1{\frac C{x^6}-\frac6{5x}}
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so the solution is

y=\dfrac{5x^6}{\frac{4131}2-6x^5}=\dfrac{10x^6}{4131-12x^5}

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3 years ago
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Answer:

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Step-by-step explanation:

3 0
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