Solve the following differential equations:
Given Differential Equation is :
⇒
⇒ ……(1)
Let us assume z = x + y + 1
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)
⇒ z – log(z + 1) = x + C
Since z = x + y we substitute this,
⇒ x + y–log(x + y + 1) = x + C
⇒ y–log(x + y + 1) = C
⇒ y = log(x + y + 1) + C
∴ The solution for the given Differential Equation is y = log(x + y + 1) + C.