markosheehan Posted June 3, 2016 Share Posted June 3, 2016 given the differential equation dy/dx=y cosx find the general solution given that y=2 when x= π /6 i cant solve this Link to comment Share on other sites More sharing options...
ajb Posted June 3, 2016 Share Posted June 3, 2016 What steps have you tried so far? A big hint is that the differential equation is separable. Link to comment Share on other sites More sharing options...
studiot Posted June 3, 2016 Share Posted June 3, 2016 (edited) 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 Link to comment Share on other sites More sharing options...
imatfaal Posted June 3, 2016 Share Posted June 3, 2016 Should this be posted in homework? Yes. Done Link to comment Share on other sites More sharing options...
Keen Posted June 4, 2016 Share Posted June 4, 2016 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. Link to comment Share on other sites More sharing options...
markosheehan Posted June 4, 2016 Author Share Posted June 4, 2016 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 Link to comment Share on other sites More sharing options...
studiot Posted June 4, 2016 Share Posted June 4, 2016 (edited) 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 Link to comment Share on other sites More sharing options...
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