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)
⇒
⇒ z – tan–1z = x + C
Since z = x + y, we substitute this,
⇒ x + y – tan–1(x + y) = x + C
⇒ y – tan–1(x + y) = C
∴ The solution for the given Differential equation is y – tan–1(x + y) = C.