Suppose y=y(x) be the solution curve to the differential equation (d y)/(d x)-y=2-e⁻ˣ such that lim x → ∞ y(x) is finite. If a and b are respectively the x - and y -intercepts of the tangent to the curve at x=0, then the value of a-4 b is equal to _ _ _ _ _ _ _.

Differential Equations: JEE Main 2022 Mathematics question

JEE Main 2022 · 26 Jul, Evening shift · Q34

JEE Main 202226 Jul, Evening shiftMathematicsMediumDifferential Equations163× since 2002

Suppose

y=y(x)

be the solution curve to the differential equation

\frac{d y}{d x}-y=2-e^{-x}

such that

\lim\limits_{x \rightarrow \infty} y(x)

is finite. If

a

and

b

are respectively the

x

- and

y

-intercepts of the tangent to the curve at

x=0

, then the value of

a-4 b

is equal to _____________.

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