Question

dy/dx+y tan x=e^x cos x​

Answer 1

dy/dx+y x=e^x cos x

hope.it helps you

Answer 2

Answer:

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Step-by-step explanation:

Given,  

dx

dy

​  

−ytanx=e  

x

secx

It is a first-degree linear D.E of the form  

 

dx

dy

​  

+Py=Q

here    P=−tanxQ=e  

x

secx

I.F=e  

∫pdx

=e  

∫−tanxdx

=e  

−log∣secx∣

 

=e  

logcosx

=cosx

The solution is given by,

y×I.F=∫Q×I.Fdx+c

⇒y×cosx=∫e  

x

secx×cosxdx+c

⇒ycosx=∫e  

x

dx+c

⇒ycosx=e  

x  +c