integration

[markosheehan]

given the differential equation dy/dx=y cosx

find the general solution given that y=2 when x= π /6

i cant solve this

[ajb]

What steps have you tried so far? A big hint is that the differential equation is separable.

[studiot]

 

find the general solution given that y=2 when x= π /6

 

Do you understand the difference between the general solution of original differential equation and

the general solution of the the problem which includes the above boundary condition?

Knowing this will help you make sense of ajb's hint

 

Should this be posted in homework?

Edited June 3, 2016 by studiot

[imatfaal]

Should this be posted in homework?

 

Yes. Done

[Keen]

The best hint I can give you is that for any interval I and any function y positive on I: dy/dx=y (d ln(y)/dx) with ln being the natural logarithm. With that, you should be able to solve it.

[markosheehan]

yes i tried integration \frac{dy}{y}= cos(x)dx but then i get ln(2)=sinx+c and then when i put in 2 for y and π /6 for x i get ln(2)=1/2 + c and this is not the answer the answer is y=2e^sinx-0.5

[studiot]

You haven't finished manipulating the integrand.

[math]\frac{{dy}}{{dx}} = y\cos (x)[/math]

rearrange to separate variables as ajb

 

[math]\frac{{dy}}{y} = \cos (x)dx[/math]

 

Integrate

 

[math]\ln (y) = A\sin (x) + B[/math]

 

take exponentials of both sides

 

[math]\exp (\ln (y)) = A\exp (\sin (x) + B)[/math]

 

That is

 

[math]y = C{e^{(\sin (x) + B)}}[/math]

 

 

Now substitute for y and x

Edited June 4, 2016 by studiot