JEE Mains · Maths · STD 12 - 9. differential equations
Let \(f\) be a differentiable function such that \(x ^2 f ( x )- x =4 \int \limits_0^x t f(t) d t, f(1)=\frac{2}{3}\).Then \(18 f(3)\) is equal to \(......\).
- A \(160\)
- B \(210\)
- C \(180\)
- D \(150\)
Answer & Solution
Correct Answer
(A) \(160\)
Step-by-step Solution
Detailed explanation
Differentiate the given equation \(\Rightarrow 2 x f(x)+x^2 f^{\prime}(x)-1=4 x f(x)\) \(\Rightarrow x^2 \frac{d y}{d x}-2 x y=1\) \(\Rightarrow \frac{d y}{d x}+\left(-\frac{2}{x}\right) y=\frac{1}{x^2}\) \(I F .=e^{\int-\frac{2}{x} t n x}=\frac{1}{x^2}\)…
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