Mathematics · 2025
JEE Main · 8 April 2025, Shift 2 · Q20
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) is
Let $\displaystyle f(x)=x-1$ and $\displaystyle g(x)=e^x$ for $\displaystyle x \in \mathbb{R}$. If $\displaystyle \frac{d y}{d x}=\left(e^{-2 \sqrt{x}} g(f(f(x)))-\frac{y}{\sqrt{x}}\right), y(0)=0$, then $\displaystyle y(1)$ is
Official answer
From NTA’s final answer key for this paper.
(1)
$\displaystyle \frac{e-1}{e^4}$
More from Differential Equations
- Let f: R → R be a thrice differentiable odd function satisfying f^′(x) ≥ 0, f^′ ′(x)=f(x), f(0)=0, f^′(0)=3. Then 9 f( log_e 3) is equal to ____.2025
- Let for some function y=f(x), ∫_0^x t f(t) d t=x^2 f(x), x>0 and f(2)=3. Then f(6) is equal to2025
- Let f:[1, ∞) →[2, ∞) be a differentiable function. If 10 ∫_1^x f(t) dt=5 x f(x)-x^5-9 for all x ≥ 1, then the value of f(3) is:2025
- Let y=y(x) be the solution curve of the differential equation (1+ sin x) (d y)/(d x)+(y+1) cos x=0, y(0)=0. If the curve y=y(x) passes through the…2026
- Let y=y(x) be the solution of the differential equation x √(1-x^2) d y+(y √(1-x^2)-x cos^-1 x) d x=0, x ∈(0,1), lim_x → 1^- y(x)=1. Then y(1/2)…2026
- Let y=y(x) be the solution of the differential equation sec x (d y)/(d x)-2 y=2+3 sin x, x ∈(-(π)/2, (π)/2), y(0)=-7/4. Then y((π)/6) is equal to:2026
- Let y=y(x) be the solution curve of the differential equation (1+x^2) d y+(y- tan^-1 x) d x=0, y(0)=1. Then the value of y(1) is:2026
- Let f: R → R be such that f(x y)=f(x) f(y), for all x, y ∈ R and f(0) ≠ 0. Let g:[1, ∞) → R be a differentiable function such that x^2 g(x)=∫_1^x(t^2…2026
JEE Main 2025 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.