JEE Mains · Maths · STD 12 - 9. differential equations
Let \(y=y(x)\) be the solution of the differential equation \(x^3 d y+(x y-1) d x=0, x>0\), \(y\left(\frac{1}{2}\right)=3-e\). Then \(y(1)\) is equal to
- A \(1\)
- B \(e\)
- C \(2- e\)
- D \(3\)
Answer & Solution
Correct Answer
(A) \(1\)
Step-by-step Solution
Detailed explanation
\(\frac{d y}{d x}=\frac{1-x y}{x^3}=\frac{1}{x^3}-\frac{y}{x^2}\) \(\frac{d y}{d x}+\frac{y}{x^2}=\frac{1}{x^3}\) \(\text { If }=e^{\int \frac{1}{x^2} d x}=e^{-\frac{1}{x}}\)…
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