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

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

Grade:12

3 Answers

Badiuddin askIITians.ismu Expert
147 Points
11 years ago

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=et  

or  dt/dx    -x et = 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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Tapasranjan Das
19 Points
11 years ago

Hi Deepak,

dy/dx=exey

=>dy/ey=exdx

=>e-ydy=exdx

=>∫e-ydy=∫exdx

=>-e-y=ex+C

Deepak Aggarwal
8 Points
11 years ago

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=et 

Please check this one out.

Thnks anyways.

     

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