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.