Solving Integral Equation: x(t) = -8?

brusier
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Homework Statement



I integrated dx/dt = x^2+(1/81)

Homework Equations



My result; 9(arctan(9x))= t+C needed to be solved for initial condition x(0)=-8
and fit into x(t) = format

The Attempt at a Solution



I cannot figure out why the computer is not accepting my solution:
arctan (9x)= (t-14.012)/9
 
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Wouldn't that be:

x(t)=\frac{(tan(\frac{t-14.012}{9}))}{9}
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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