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,
⇒
⇒
⇒
⇒
⇒
⇒
Integrating on both sides we get,
⇒
We know that:
(1) ∫adx = ax + C
(2)
⇒ 2z – log(z + 3) = x + C
Since z = x – y, we substitute this,
⇒ 2(x – y) – log(x–y + 3) = x + C
⇒ 2x – 2y –log(x–y + 3) = x + C
⇒ x – 2y –log(x–y + 3) = C
∴ The solution for the given Differential equation is: x – 2y –log(x–y + 3) = C.