JEE Mains · Maths · STD 12 - 9. differential equations
Let \(f:(0, \infty) \rightarrow \mathbf{R}\) be a function which is differentiable at all points of its domain and satisfies the condition \(x^2 f^{\prime}(x)=2 x f(x)+3\), with \(f(1)=4\). Then \(2 f(2)\) is equal to :
- A 39
- B 19
- C 29
- D 23
Answer & Solution
Correct Answer
(A) 39
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & x^2 f^{\prime}(x)-2 x f(x)=3 \\ & \left(\frac{x^2 f^{\prime}(x)-2 x f(x)}{\left(x^2\right)^2}\right)=\frac{3}{\left(x^2\right)^2} \\ & \Rightarrow \frac{d}{d x}\left(\frac{f(x)}{x^2}\right)=\frac{3}{x^4}\end{aligned}\) Integrating both sides…
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