Solving a Differential Equation with Initial Conditions

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Find the particular solution satisfying the initial condition y(0)=0

dy/dx + 2y = 5






The Attempt at a Solution


- I have absolutely no clue where to start. I have a terrible teacher and the book we're using is very poor. If anyone can help me out, that would be great.
 
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Can't you give some attempt in solving this? You know the meaning of a derivative, otherwise you would not be working on differential equations, that's a start. Next you know that you should look for a function and not a certain value. So in order to get to this unknown function you have to do something. Can you tell us what?

I can help you through this if you want. Just follow it step by step. First what do you need to do to get to the unknown function?
 

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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