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Differential Equations question

2024 · 9 Apr · Shift 2 · Q54

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JEE Main
Mathematics
Differential Equations
2024 · 9 Apr · Shift 2 · Q54

Differential Equations question

2024 · 9 Apr · Shift 2 · Q54

JEE MainMathematicsDifferential EquationsNumerical+4 / −1

For a differentiable function

f: \mathbb{R} \rightarrow \mathbb{R}

, suppose

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

, where

\alpha \in \mathbb{R}, f(0)=1

and

\lim_{x \rightarrow-\infty} f(x)=7

. Then

9 f\left(-\log _e 3\right)

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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