NDA 2018 Maths · Mathematics · Differential Equations · medium

The function y=Ae^x+Be^-x satisfies the differential equation (d^2y)/(dx^2-y=0. 2. The differential equation of all circles centred at the origin is…

Single correct option

Consider the following statements:
1. The function

y=Ae^x+Be^{-x}

satisfies the differential equation

\frac{d^2y}{dx^2}-y=0

.
2. The differential equation of all circles centred at the origin is

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

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

Show answer and solution

Answer: (C) Both 1 and 2

For statement 1,

y''=Ae^x+Be^{-x}=y

, so

y''-y=0

holds. For statement 2, differentiate

x^2+y^2=r^2

to get

2x+2yy'=0

, i.e.

x+yy'=0

, with the arbitrary radius eliminated. Both statements are correct.

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