Q. 25.0( 1 Vote )

Solve the following differential equations:


Answer :

Given Differential equation is:




……(1)


Let us assume z = x – y


Differentiating w.r.t x on both sides we get,




……(2)


Substituting (2) in (1) we get,




Bringing like variables on same side (i.e., variable seperable technique) we get,







We know that cos2z = cos2z – sin2z = 2cos2z – 1 = 1 – 2sin2z.





We know 1 + cot2x = cosec2x




Integrating on both sides we get,



We know that:


(1) ∫cosec2x = –cotx + C


(2)


(3) ∫adx = ax + C




Since z = x – y substituting this we get,



The solution for the given Differential equation is .


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