Find an explicit solution of the IVP...

[hank]

Ok, so I need to do that for:
dx/dt = 4(x^2 + 1) and x(pi/4) = 1

So,
dx = 4(x^2 + 1) dt
dx/(x^2 + 1) = 4 dt

After integrating both sides:
invtan(x) = 4t + c where invtan is inverse tan

<math happens>

x = tan (4t - 3pi/4)

Can someone fill in the math happens step(s) for me?


Thanks.

 

[Deleted member 4993]

Ok, so I need to do that for:
dx/dt = 4(x^2 + 1) and x(pi/4) = 1

So,
dx = 4(x^2 + 1) dt
dx/(x^2 + 1) = 4 dt

After integrating both sides:
invtan(x) = 4t + c where invtan is inverse tan

This comes from the definition of "inverse tan". Do you know the definition of inverse tan? If you do - can you please tell us what it is? If you don't, look it up in your textbook and/or google it - then tell us what you learnt.

In addition, you'll need to apply your given boundary condition. Your boundary condition tells us, at t = 1, x(t) = ?/4.


<math happens>

x = tan (4t - 3pi/4)

Can someone fill in the math happens step(s) for me?


Thanks.