( ( e^( -2( X^(1/2) ) ) / x^(1/2) ) - (dx/dy) = 1

[mrgthiru]

Solve the differential equation...

( ( e^( -2( X^(1/2) ) ) / x^(1/2) ) - (dx/dy) = 1

Could any one help me plz....

 

[Deleted member 4993]

Are you sure you had dx/dy in your equation and not 'dy/dx'?

substitute

z = x^(1/2)

dz/dx = 1/(2*z)

Now continue...

Show your work if you need further help.

 

[morson]

Just integrate each term-by-term:

For the first integral, let \(\displaystyle \L\ u = -2\sqrt{x}\\), so \(\displaystyle du = -\frac{dx}{\sqrt{x}\\)

So the first integral becomes: \(\displaystyle \L\ \int -e^u\ du\) = $\displaystyle D - e^u$

So, \(\displaystyle \L\ D - e^u - y = x + C\), therefore: \(\displaystyle \L\ y = A - e^{-2\sqrt{x}} - x\)