Differential EquationHard

Question

Ifty(t)dt = x2 + y(x) then y as a function of x is-

Options

A.y = 2 - (2 + a2)e
B.y = 1 - (2 + a2)e
C.y = 2 - (1 + a2)e
D.none

Solution

y(t)dt = x + y(x)
⇒ xy = 2x + ⇒ x(y - 2) =
⇒ ∫xdx = ln|y - 2| + lnc
⇒ ex2/2 = c(y - 2)
at x = a        Y = - a2
∴ ex2/2 = c(-a2 - 2) ⇒ c = -
∴ (y - 2)
⇒ - y + 2 = (a2 + 2)e
⇒ y = 2 - (2 + a2)e

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