Solve the differential equation: dy/dx = e^(xy)

Dear DEEPAK

dy/dx = e^(xy)

let xy=t

 xdy/dx + y =dt/dx

or  xdy/dx + t/x =dt/dx

or  dy/dx = 1/x dt/dx - t/x²

so question become     

1/x dt/dx  -1/x²=e^t  

or  dt/dx    -x e^t = 1/x

so I.F= e^∫-xdx 

           =e^-_x2_/2

    so  t.e^-_x2_/2   = ∫1/x e^-_x2_/2   dx   +c

now it is simple intigration

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Badiuddin

Hi Deepak,

dy/dx=e^xe^y

=>dy/e^y=e^xdx

=>e^-ydy=e^xdx

=>∫e^-ydy=∫e^xdx

=>-e^-y=e^x+C

Badiuddin sir, actually see the 5th step after u have written the question became. there i think u missed a 't'. actually there the question become

1/x dt/dx  - t/x²=e^t 

Please check this one out.

Thnks anyways.