JEE Mains · Maths · STD 12 - 9. differential equations
Let \(y(x)\) be the solution of the differential equation \(\left( {xlogx} \right)\frac{{dy}}{{dx}} + y = 2xlogx,\left( {x \ge 1} \right)\) . Then \(y(e) \) is equal to : \([y(1)=0]\)
- A \(2e\)
- B \(e\)
- C \(0\)
- D \(2\)
Answer & Solution
Correct Answer
(D) \(2\)
Step-by-step Solution
Detailed explanation
\((x \log x) \frac{d y}{d x}+y=2 x \log x\), \(\Rightarrow \quad \frac{d y}{d x}+\frac{y}{x \log x}=2\) This is a linear differential equation. \({\rm{IF}} = {e^{\int {\frac{1}{{x\log x}}} }}dx = {e^{\log \log x)}} = \log x\) Now, the solution of given diffterential equation is…
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