Statement-1 Given differential equations are dxdy+y2=x and dx2d2y+y=sinx Their degrees are 1 . Both have equal degree. Also, Statement −2 is the correct explanation for Statement - 1.
JEE Main 2012 — Mathematics Calculus
Statement 1: The degrees of the differential equations dxdy+y2=x and dx2d2y+y=sinx are equal. Statement 2: The degree of a differential equation, when it is a polynomial equation in derivatives, is the highest positive integral power of the highest order derivative involved in the differential equation, otherwise degree is not defined.
Held on 12 May 2012 · Verified 6 Jul 2026.
Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.
Statement 1 is false, Statement 2 is true.
Statement 1 is true, Statement 2 is false.
Statement 1 is true, Statement 2 is true; Statement 2 is a correct explanation of Statement 1.
Sign in to track your attempts and accuracy.
Sign in to keep a private note on this question. Nothing you write is ever public.
Let $[\cdot]$ denote the greatest integer function. Then the value of $\displaystyle\int_0^3 \left(\dfrac{e^x + e^{-x}}{[x]!}\right) dx$ is :
The value of $\sum_{r=1}^{20}\left(\left|\sqrt{\pi\left(\int_{0}^{r} x|\sin \pi x| d x\right)}\right|\right)$ is $\_\_\_\_$
The value of ∫₀¹ x·eˣ dx is:
If the area of the region bounded by $16x^2 - 9y^2 = 144$ and $8x - 3y = 24$ is A, then $3(A + 6 \log_e(3))$ is equal to _______.
Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a differentiable function such that $f\left(\dfrac{x+y}{3}\right) = \dfrac{f(x) + f(y)}{3}$ for all $x, y \in \mathbb{R}$, and $f'(0) = 3$. Then the minimum value of the function $g(x) = 3 + e^x f(x)$, is:
Work through every JEE Main Calculus PYQ, year by year.