Given differential equation, ydx−xdy−3y2dy=0
⇒ dydx=yx+3y
dydx−yx=3y
I.F. = e−∫y1dy=e−lny=y1
∴ solution is
yx=∫3y.y1dy
⇒ yx=3y+c
Passes through (1,1),
∴1=3+c;c=−2
Equation of required curve, x=3y2−2y
Clearly, it passes through (3−1,31).
JEE Main 2017 — Mathematics Calculus
The curve satisfying the differential equation, ydx−(x+3y2)dy=0 and passing through the point (1,1) also passes through the point
Held on 8 Apr 2017 · Verified 6 Jul 2026.
(41,−21)
(−31,31)
(41,21)
(31,−31)
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.