JEE Main 2018 — Differential Equations Question with Solution
From: JEE Main 2018 (Offline)
Question
Let y = y(x) be the solution of the differential equation
, .
If , then is equal to :
, .
If , then is equal to :
Choose an option
Show full solutionCorrect option: D
Correct answer
D
Step-by-step explanation
Given,
sin x
+ y cot x = 4x cosec x
This is a linear differential equation of form,
+ py = Q
Where p = cot x and Q = 4x cosec x
So, Integrating factor (I. F)
=
=
=
=""
= sin x as
Solution of the differential equation is
y sin x = 4x cosecx sinx dx + c
y sinx =
y sinx = 4.
y sinx = 2x2 + c . . . . . (1)
Given that,
x = and y = 0
Put this x = and y = 0 at equation (1)
0.1 = 2. 2 + c
c =
So, differential equation is
y sin x = 2x2
Now we have to find y
So, put x = at equation (2)
y . sin = 2
= 2.
sin x
+ y cot x = 4x cosec x
This is a linear differential equation of form,
+ py = Q
Where p = cot x and Q = 4x cosec x
So, Integrating factor (I. F)
=
=
=
= sin x as
Solution of the differential equation is
y sin x = 4x cosecx sinx dx + c
y sinx =
y sinx = 4.
y sinx = 2x2 + c . . . . . (1)
Given that,
x = and y = 0
Put this x = and y = 0 at equation (1)
0.1 = 2. 2 + c
c =
So, differential equation is
y sin x = 2x2
Now we have to find y
So, put x = at equation (2)
y . sin = 2
= 2.
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This is a previous-year question from JEE Main 2018, covering the Differential Equations chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.