NDA 2023 Maths · Mathematics · Differential Equations · easy

Y=e^2x satisfies the equation (d^2y)/(dx^2-4y=0. 2. y=sin x satisfies the equation (d^2y)/(dx^2+y=0.

Single correct option

Consider the following statements:
1.

y=e^{2x}

satisfies the equation

\dfrac{d^2y}{dx^2}-4y=0

.
2.

y=\sin x

satisfies the equation

\dfrac{d^2y}{dx^2}+y=0

.
Which of the statements given above is/are correct?

Show answer and solution

Answer: (C) Both 1 and 2

For

y=e^{2x}

y''=4e^{2x}=4y

, so

y''-4y=0

and Statement 1 is true. For

y=\sin x

y''=-\sin x

, so

y''+y=0

and Statement 2 is true. Both functions satisfy their respective equations.

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