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If dy/dx=y/x and y(1)=2, then y(3) is equal to Single correct option
If
d y d x = y x \dfrac{dy}{dx}=\dfrac yx d x d y = x y and
y ( 1 ) = 2 y(1)=2 y ( 1 ) = 2 , then
y ( 3 ) y(3) y ( 3 ) is equal to
A. 6 6 6 B. 5 5 5 C. 9 9 9 D. 18 18 18 Show answer and solution Answer: (A) 6 6 6
Separate variables:
d y y = d x x \frac{dy}{y}=\frac{dx}{x} y d y = x d x , so
ln y = ln x + ln c \ln y=\ln x+\ln c ln y = ln x + ln c , i.e.
y = c x y=cx y = c x . From
y ( 1 ) = 2 y(1)=2 y ( 1 ) = 2 ,
c = 2 c=2 c = 2 and
y = 2 x y=2x y = 2 x , so
y ( 3 ) = 6 y(3)=6 y ( 3 ) = 6 . The value
9 9 9 comes from
y = x 2 + … y=x^2+\dots y = x 2 + … ,
5 5 5 from
y = x + 2 y=x+2 y = x + 2 , and
18 18 18 from
y = 2 x 2 y=2x^2 y = 2 x 2 , none of which satisfy the equation.
Original question written in the NDA 2025 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