Consider the differential equation dy/dx+2y=0 ;

Correct Answer is : all solutions of equation approaches to zero when x→∞x arrow ∞x→∞.

every solution of equation is identically zero.

all solutions of equation are unbounded.

all solutions of equation approaches to zero when x arrow ∞.

no solution of equation approaches to zero when x arrow ∞.

Correct Answer is : all solutions of equation approaches to zero when x→∞x arrow ∞x→∞.

Test Index

PUNE MCA Exam 2015 Question Paper with answers for online practice

Question : 3 of 59

Marks: +1, -0

\frac{dy}{dx}+2y=0

;

Solution:

Concept:

The differential equation is first-order linear homogeneous, leading to exponential decay solutions.

Explanation:

The equation is

\frac{dy}{dx} + 2y = 0

Separate variables:

\frac{dy}{y} = -2 dx

Integrate:

\ln|y| = -2x + C

, so

y = e^{-2x + C} = A e^{-2x}

, where

A = e^C

is a constant.

x \rightarrow \infty

e^{-2x} \rightarrow 0

, hence

y \rightarrow 0

for any finite

A

Thus, all solutions tend to zero at infinity.

Answer:

Option C is correct.

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