Solve This Differntial Equation.

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1. dy/dx = 5-3y^2

y(0)=2



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3. I just don't know where to start.Should I Differentiate again Or Use Bernoulli Eqn.PLZ HELP ME ASAP
 
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That's a simple "separable" equation. Separate x and y and integrate.
 
ok thanks mate!
 
fan_103 said:
1. dy/dx = 5-3y^2

y(0)=2

I just don't know where to start.Should I Differentiate again Or Use Bernoulli Eqn.PLZ HELP ME ASAP
When you're trying to solve a differential equation, you already have something involving the derivative of a function, so differentiating again wouldn't be a wise strategy.
 
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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