Q. 55.0( 1 Vote )

# Solve the following differential equations:

Answer :

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^{–1}z = 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**.

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