NDA 2017 Maths · Mathematics · Differential Equations · hard

The integrating factor of dy/dx+y/x=x^2 is x. 2. The differential equation of the family y=Ae^2x+Be^-2x is (d^2y)/(dx^2+4y=0.

Single correct option

Consider the following statements:
1. The integrating factor of

\dfrac{dy}{dx}+\dfrac yx=x^2

x

.
2. The differential equation of the family

y=Ae^{2x}+Be^{-2x}

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

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

Show answer and solution

Answer: (A) 1 only

1: IF

=e^{\int dx/x}=x

; true. 2: differentiating twice,

y''=4Ae^{2x}+4Be^{-2x}=4y

, so the equation is

y''-4y=0

, not

y''+4y=0

(that belongs to

\sin2x,\cos2x

). Only statement 1 is correct.

Original question written in the NDA 2017 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake