I have the following to problem:-(adsbygoogle = window.adsbygoogle || []).push({});

1)dy/dt = (1+y^2)/(1+4t^2) y(0)=1

This equation is seperable I arrive at

Integral 1/(1+y^2) dy = Integral 1/(1+4t^2) dt

If I let 2t=x then the RHS is in the same form as my standard integrals.

Which is Integral 1/(x^2 + a^2) = 1/a arctan(x/a)

So far so good methinks...

After a bit of 'jiggery pokery' I get

arctan(y) = arctan(2t) + C

Take tan of both sides -> y = 2t + tan(C)

Putting in initial values

1 = 2*0 + tan(C)

Therefore C = pi/4

Finally y = 2t + pi/4 -> Am I right!!

Now my second equation is thus:

(x^2 + 1)dy/dx -2xy = 2x(x^2 +1)

Putting it into standard from

dy/dx - (2xy)/(x^2 + 1) = 2x

This gives me an integrating factor 1/(x^2 +1)

Now what!?

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# Homework Help: Differential equations

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