Do I Need to Divide the Constant and Term in Separation of Variables?

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Im doing separation of variables now and I am stuck...ive come up to this stage

-5 ln 2-3i = t^2/2 + C

my problem is do i need to divide the C and t^2/2 by -5? or don't divide the C?

please help me..
thnks
 
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You need an initial condition.
 
sorry i don't get it...im trying to make the general solution...from the question i(0) = 12
 
So setting t=0 shows that -5ln|2-3*i(0)|=C=> -5ln|2-36|=C=>-5ln(34)=C, so substitute this into your equation.
 
ok thanks for the help
 

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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