JEE Mains · Maths · STD 12 - 9. differential equations
Let \(f\) be a differentiable function in the interval \((0, \infty)\) such that \(f(1)=1\) and \(\lim _{t \rightarrow x} \frac{t^2 f(x)-x^2 f(t)}{t-x}=1\) for each \(x>0\). Then \(2 f(2)+3 f(3)\) is equal to ....................
- A \(25\)
- B \(24\)
- C \(26\)
- D \(48\)
Answer & Solution
Correct Answer
(B) \(24\)
Step-by-step Solution
Detailed explanation
\( \lim _{t \rightarrow x} \frac{t^2 f(x)-x^2 f(t)}{t-x}=1 \) \( \lim _{t \rightarrow x} \frac{2 t . f(x)-x^2 f^{\prime}(x)}{1}=1 \) \( 2 x . f(x)-x 2 f^{\prime}(x)=1 \) \( \frac{d y}{d x}-\frac{2}{x} \cdot y=\frac{-1}{x^2} \)…
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