1st order ODE, Reduction to Separable Form Help required

Hey guys,

I'm very new to this form of solving differential equations and I've come to a stump in a problem.

The problem is simply to find the general solution to

I have a guide that also shows the steps to the solution, but the area I am stuck on is identical to the guide, where i don't see how it got from one step to the next.

This is what I have so far;

Set

Therefore;

Now, at this point I assumed it would be very easy to separate the variables to;

And solve by integration. However, the guide goes from

to

My question is... what step am i missing that u becomes 2u and 4/x becomes 8/x?

Thanks for your time

Re: 1st order ODE, Reduction to Separable Form Help required

Quote:

Originally Posted by

**Nuingaer** Hey guys,

I'm very new to this form of solving differential equations and I've come to a stump in a problem.

The problem is simply to find the general solution to

I have a guide that also shows the steps to the solution, but the area I am stuck on is identical to the guide, where i don't see how it got from one step to the next.

This is what I have so far;

Set

Therefore;

Now, at this point I assumed it would be very easy to separate the variables to;

And solve by integration. However, the guide goes from

to

My question is... what step am i missing that u becomes 2u and 4/x becomes 8/x?

Thanks for your time

They multiplied both sides by 2. Why, I don't know. But it's valid...

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Re: 1st order ODE, Reduction to Separable Form Help required