Very Difficulty Differential Equation

kamdad
Messages
1
Reaction score
0
Very Difficulty Differential Equation ...

(x+y)dx + xy dy=0 .

Please Solve This Problem ?
 
Physics news on Phys.org


kamdad said:
(x+y)dx + xy dy=0 .

Please Solve This Problem ?

You need to show your attempt(s) at a solution before we can help you. Please follow the template that is provided when you create a thread.
 


Adding to what Dembadon said, we provide help, but we don't do the work for you. You can see the Rules by clicking the Rules menu item near the top of the page, especially the section titled Homework Help.
 
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...
Back
Top