Mathematics · 2021
JEE Main · 17 March 2021, Shift 2 · Q68
Let y=y(x) be the solution of the differential equation cos x(3 sin x+ cos x+3) d y=(1+y sin x(3 sin x+ cos x+3)) d x, 0 ≤ x ≤ (π)/2, y(0)=0. Then,…
Let $\displaystyle y=y(x)$ be the solution of the differential equation
$\displaystyle \cos x(3 \sin x+\cos x+3) \mathrm{d} y=(1+y \sin x(3 \sin x+\cos x+3)) \mathrm{d} x, 0 \leq x \leq \frac{\pi}{2}, y(0)=0$. Then, $\displaystyle y\left(\frac{\pi}{3}\right)$ is equal to :
Official answer
(4)
$\displaystyle 2 \log _{\mathrm{e}}\left(\frac{2 \sqrt{3}+10}{11}\right)$
More from Differential Equations
- If y=y(x) is the solution of the differential equation (5+e^x)/(2+y) · (d y)/(d x)+e^x=0 satisfying y(0)=1, then a value of y( log_e 13) is:2020
- Let the solution curve y=y(x) of the differential equation (4+x^2) d y-2 x(x^2+3 y+4) d x=0 pass through the origin. Then y(2) is equal to \ \ \ \.2022
- A hostel has 100 students. On a certain day (consider it day zero) it was found that two students are infected with some virus. Assume that the rate…2022
- Let y=y(x) be the solution of the differential equation (d y)/(d x)=2 x(x+y)^3-x(x+y)-1, y(0)=1. Then, (1/(√2)+y(1/(√2)))^2 equals:2024
- Let y=y(x) be the solution of the differential equation (x+y+2)^2 d x=d y, y(0)=-2. Let the maximum and minimum values of the function y=y(x) in [0,…2024
- Let C_1 be the curve obtained by the solution of differential equation 2 x y (d y)/(d x)=y^2-x^2, x>0. Let the curve C_2 be the solution of (2 x…2021
- Let f(x)=x-1 and g(x)=e^x for x ∈ R. If (d y)/(d x)=(e^-2 √x g(f(f(x)))-y/(√x)), y(0)=0, then y(1) is2025
- Let f(x)=√(lim_r → x{(2 r^2[(f(r))^2-f(x) f(r)])/(r^2-x^2)-r^3 e^((f(r))/r)}) be differentiable in (-∞, 0) ∪(0, ∞) and f(1)=1. Then the value of e a,…2024
JEE Main 2021 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.