# Differential Equations

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Solve the seperable differential equation for U.

du/dt = e^(5u+7t) - Using the following initial condition U(0) = 12

• Differential Equations -

du/dt = e^5u * e^7t

du/e^5u = e^7t dt

e^-5u du = e^7t dt

(1/-5) e^-5u = (1/7) e^7t + C

7 e^-5u = -5 e^7t + c

when t = 0, u = 12
7 e^-60 = -5 + c
c = 5 +7/e^60 or c is about 5

7 e^-5u + 5 e^7t = 5

• Algebra -

Solve for u
-29 + -4 + 5u

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