Solving $\frac{dx}{dz}-\frac{2x}{z}=1$ [closed]

Please can someone solve this?

$$\frac{dx}{dz}-\frac{2x}{z}=1$$

Please this is only part of my homework question. I am stuckwith here. Please teach me this solution thank you:)

Solution 1:

To elaborate on Amzoti's suggestion:

Here is a nice step-by-step solution to help you work through your problem.

Do take the time to study (refresh your memory) about integrating factors, and how to use them for problems of this type, so you can apply this technique to a wider range of such problems.

Solution 2:

Hint: Try Integrating Factor:

$$\mu(z) = e^{-\int 2/z~ dz} = \dfrac{1}{z^2}$$

See referenced web site for examples if you are not clear on this technique.

Solution 3:

The homogenous equation is $$\frac{dx}{dz}-\frac{2x}{z}=0\iff 2\frac{dz}{z}=\frac{dx}{x}$$ and by integration we have the solution $$x:z\mapsto Cz^2$$ and for the particular solution the function $z\mapsto -z$ is a remarquable solution so the general solution is $$x:z\mapsto Cz^2-z$$