Let y(x) be the solution of the differential equation (x log x) \frac{dy}{dx}+ y = 2x log x, (x \geq 1). Then y(e) is equal to

Engineering

Mathematics

Linear Differential Equation

Question

Let y(x) be the solution of the differential equation (x log x) $\frac{dy}{dx}$ + y = 2x log x, (x $\geq$ 1). Then y(e) is equal to

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

Integrating factor = ℓn x

$∴$ General solution is

y (ℓn x) = 2(x ℓn x – x) + c

Put x = 1, we get c = 2

$∴$ y(e) = 2