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 the like variables to same side (i.e., Variable seperable technique) we get,
⇒
Integrating on both sides we get,
⇒
⇒
We know that:
(1)
(2)
⇒
⇒ tan–1z = x + C
Since z = x + y we substitute this,
⇒ tan–1(x + y) = x + C
⇒ x + y = tan(x + C)
∴ The solution for the given Differential equation is x + y = tan(x + C).