JEE MATHEMATICS MCQ: DIFFERENTIAL EQUATIONS

1 Easy

1 of 1

Analyzing +4 | -1

Let

f(x)

be differentiable on the interval

(0, \infty)

such that

f(1)=1

, and

\lim\limits _{t \rightarrow x} \frac{t^2 f(x)-x^2 f(t)}{t-x}=1

for each

x>0

. Then

f(x)

View answer and explanation

Correct option: A

\frac{1}{3 x}+\frac{2}{3} x^2

Option A is correct because it satisfies the given limit condition and the initial condition f(1)=1 after solving the differential equation.

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