3 years ago

I need help someone

Mathematics

1 answer:

allochka39001 [22]3 years ago

7 0

Answer:

There is no correlation.

Step-by-step explanation:

The points are far spread and does not give any correlation.

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(1+x^2)dy/dx+2xy-4x^2=0 bu using Bernoulli's Equation

erastovalidia [21]

Not of Bernoulli type, but still linear.

$(1+x^2)\dfrac{\mathrm dy}{\mathrm dx}+2xy=4x^2$

There's no need to find an integrating factor, since the left hand side already represents a derivative:

$\dfrac{\mathrm d}{\mathrm dx}[(1+x^2)y]=(1+x^2)\dfrac{\mathrm dy}{\mathrm dx}+2xy$

So, you have

$\dfrac{\mathrm d}{\mathrm dx}[(1+x^2)y]=4x^2$

and integrating both sides with respect to $x$ yields

$(1+x^2)y=\displaystyle\int4x^2\,\mathrm dx$
$(1+x^2)y=\dfrac43x^3+C$
$y=\dfrac{4x^3}{3(1+x^2)}+\dfrac C{1+x^2}$