Solve the Separable Differential Equation for u

jwj11
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Homework Statement



Solve the separable differential equation for u

du/dt = e^(6u + 8t)

Use the following initial condition: u(0) = 13.

Homework Equations



Techniques for solving separable differential equations.

1. Group variable and respective dy,dx,dz, etc. together
2. Integrate both sides
3. Solve for C using given data point
4. Solve for dependent variable

The Attempt at a Solution



http://img177.imageshack.us/img177/7321/differentialequation.jp
 
Last edited by a moderator:
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It isn't incorrect. What makes you think otherwise?
 
Hmm.. I guess I am inputting it wrong. This is part of a webwork assignment (an online submission assignment)
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

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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