EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 31 - Differential Equations>JEE Main - 1 February 2023 Shift 1>Q 141

HARD

JEE Main

IMPORTANT

Earn 100

If $y = y (x)$ is the solution curve of the differential equation $\frac{d y}{d x} + y \tan x = x \sec x, 0 \leq x \leq \frac{π}{3}, y (0) = 1$ , then $y (\frac{π}{6})$ is equal to

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Important Questions on Differential Equations

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 31 - Differential Equations>JEE Main - 1 February 2023 Shift 1>Q 142

Let

f : ℝ \to ℝ

be a differentiable function such that

f^{'} (x) + f (x) = \int_{0}^{2} f (t) d t

. If

f (0) = e^{- 2}

, then

2 f (0) - f (2)

is equal to _____ .

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 31 - Differential Equations>JEE Main - 1 February 2023 Shift 2>Q 143

Let

α x = \exp (x^{β} y^{γ})

be the solution of the differential equation

2 x^{2} y d y - (1 - x y^{2}) d x = 0

,

x > 0, y (2) = \sqrt{\log_{e} 2}

. Then

α + β - γ

equals :