Question

solve the differential equation:
dy/dx=(√y)cos^2(√y)

Answer 1

WHO WILL HELP ME?

Answer 2

This equation is separable:
\[ \int \frac{dy}{\sqrt{y}\ \ \cos^2 \sqrt{y}} = \int dx \]

Now substitute \( u = \sqrt{y} \).

Answer 3

Ummmm but I will face a problem with "cot^2"

Answer 4

No, with sec^2. And this is the standard derivative of another trig function.

Answer 5

\[ (d/dx) \tan x = \sec^2 x \]

Answer 6

Ok.. I will try to solve it.. but just give me "final result"

Answer 7

My dear!! where are you?

Answer 8

Are you still facing a problem?

Answer 9

dy/dx=(√y)cos^2(√y)
\[\int\limits_{}^{}dy/\sqrt{y }\cos^2 \sqrt{y}= \int\limits_{}^{}dx\]

Answer 10

\[\int\limits_{}^{}\sec^2 \sqrt{y}dy/\sqrt{y}=x+C\]

Answer 11

\[2\tan \sqrt{y}=x+C\]
y=[tan^-1 (x+C)/2]^2

Answer 12

mark 0 ,,, Thank so much..