Let \( y = y(x) \) be the solution of the differential equation:
\[ \frac{dy}{dx} + \left( \frac{6x^2 + (3x^2 + 2x^3 + 4)e^{-2x}}{(x^3 + 2)(2 + e^{-2x})} \right)y = 2 + e^{-2x}, \quad x \in (-1, 2) \]
satisfying \( y(0) = \frac{3}{2} \).
If \( y(1) = \alpha \left(2 + e^{-2}\right) \), then the value of \( \alpha \) is ________.
Let \( y = y(x) \) be the solution of the differential equation:
\[ \frac{dy}{dx} + \left( \frac{6x^2 + (3x^2 + 2x^3 + 4)e^{-2x}}{(x^3 + 2)(2 + e^{-2x})} \right)y = 2 + e^{-2x}, \quad x \in (-1, 2) \]
satisfying \( y(0) = \frac{3}{2} \).
If \( y(1) = \alpha \left(2 + e^{-2}\right) \), then the value of \( \alpha \) is ________.
- \(\frac{13}{8}\)
- \(\frac{6}{13}\)
- \(\frac{12}{13}\)
- \(\frac{13}{12}\)
The Correct Option is C
Solution and Explanation
Top Questions on Differential Equations
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If \[ \frac{dy}{dx} + 2y \sec^2 x = 2 \sec^2 x + 3 \tan x \cdot \sec^2 x \] and
and \( f(0) = \frac{5}{4} \), then the value of \[ 12 \left( y \left( \frac{\pi}{4} \right) - \frac{1}{e^2} \right) \] equals to:
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