Analytic soln to 1sr order nonlinear DE

[a_huque]

Hi there,

Need some help to slove the following differential equation analytically. This nonlinear 1st order DE is neither separable nor exact. I have a feeling that there may exist a integrating factor u(x,y) that will force the DE to be exact and solvable. I have tried some standard techniques to find it but no avail.

dy/dx = -(b + cosx) + (bc - asinx)/y; where a>b>0 and c is any real (preferably positive) number.

Do appreciate your help.

Thanks much.
Abu-Sayeed

 

[Deleted member 4993]

Hi there,

Need some help to slove the following differential equation analytically. This nonlinear 1st order DE is neither separable nor exact. I have a feeling that there may exist a integrating factor u(x,y) that will force the DE to be exact and solvable. I have tried some standard techniques to find it but no avail.

dy/dx = -(b + cosx) + (bc - asinx)/y; where a>b>0 and c is any real (preferably positive) number.

Do appreciate your help.

Thanks much.
Abu-Sayeed

Apparently - it does not have simple solution.

I used Wolfram-alpha and it just gives back alternate forms instread of solutions.

May somebody with full-strength Mathematica can give it a try.

 

[galactus]

I ran this through Maple's DE solver, and it gave me "unable to obtain solution".

You have \(\displaystyle \frac{dy}{dx}=-(b+cos(x))+\frac{bc-a\cdot sin(x)}{y}\)

Is that correct?.