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Differential Equations question

2024 · 1 Feb · Shift 2 · Q44

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JEE Main
Mathematics
Differential Equations
2024 · 1 Feb · Shift 2 · Q44

Differential Equations question

2024 · 1 Feb · Shift 2 · Q44

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

Let

\alpha

be a non-zero real number. Suppose

f: \mathbf{R} \rightarrow \mathbf{R}

is a differentiable function such that

f(0)=2

and

\lim\limits_{x \rightarrow-\infty} f(x)=1

. If

f^{\prime}(x)=\alpha f(x)+3

, for all

x \in \mathbf{R}

, then

f\left(-\log _{\mathrm{e}} 2\right)

is equal to :

A
7
B
9
C
3
D
5

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