Let / be a differentiable function such that x 2 f(x)-x = …

Maths Differential Equations JEE Main 2023 Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 11, 2026

Let / be a differentiable function such that x 2 f(x)-x = f(t) dt, . Then 18f(c) is equal to

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Text Solution

Verified by Experts

The correct answer is:

Given,

x 2 f(x)-x = f(t)dt

Now Differentiating both side w.r.t. x we get,

x 2 f'(x)+2xf(x)-1 = 4xf(x)

x 2 f'(x)-l = 2x f(x)

Which is a linear differential equation,

So I.F =

Now solution of the differential equation is given by,

Now given, f(a)=

So,

Hence, the function will be,

So, the required value is given by,

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