Solve (2y + x) = 1

Question

Question

Answer 1

Concept:

In first order linear differential equation;

, where P and Q are function of x

Integrating factor (IF) = e∫ P dx

General solution: y × (IF) = ∫ Q(IF) dx

Calculation:

The given equation is

(2y + x) = 1

⇒ (2y + x) =

⇒ - x = 2y

∴ It is linear differential equation is of first order

IF = e∫ -1 dy

⇒ IF = e-y

Now, x × (IF) = ∫ Q (IF) dy

⇒ x × e-y = ∫ 2y × e-y dy

⇒ xe^-y = 2

⇒ xe-y = 2 + c

⇒ x + 2y + 2 = ce^y

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