The differential equation dy + 4y = 5dx is valid in the

The differential equation dy + 4y = 5
dx

is valid in the domain 0 ≤ x ≤ 1 with y(0) = 2.25. The solution of the differential equation is

	dy	+ 4y = 5
	dx

I.F. = e^{∫4 dx} = e^{4 x}
⇒ y × I.F. = ∫ 5 × (I.F.)dx + C

⇒ y . e^{4 x} = 5.	e^{4 x}	+ C
	4

⇒ 2.25 × 1 = 5.	e⁰	+ C
	4

⇒ C = 1

y . e^{4 x} = 5.	e^{4 x}	+ 1
	4

⇒ y =	5	+ e^{-4 x}
	4

⇒ y = e^{-4 x} + 1.25