The solution of the differential equation d x d y − k y = 0 , y ( 0 ) = 1 , approach zero when x → ∞ , if

d x d y − Ky = 0 , y d y = K d x ln y = K x + c At x = 0 , y = 1 ∴ C = 0 Now, ln y = K x y = e K x Lim x → ∞ y = Lim x → ∞ e K x = 0 ∴ K < 0

Mathematics - Differential Equation Question with Solution | TestHub

MathematicsDifferential EquationVariable separableEasy2 minQB

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The solution of the differential equation $\frac{d y}{d x} - k y = 0, y (0) = 1$ , approach zero when $x \to \infty$ , if

Answer:

Solution:

$\frac{d y}{d x} - Ky = 0, \frac{d y}{y} = K d x$

$ln y = K x + c$

At $x = 0, y = 1$ $∴ C = 0$

Now, $ln y = K x$

$y = e^{K x}$

$Lim_{x \to \infty} y = Lim_{x \to \infty} e^{K x} = 0$

$∴ K < 0$

Stream:JEESubject:MathematicsTopic:Differential EquationSubtopic:Variable separable

⏱ 2mℹ️ Source: QB

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