Solve the following differential equations:
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 .