Question:

The integrating factor of the differential equation $\frac{dy}{dx}=\frac{x^3+y^3}{xy^2}$ is

Updated On: Mar 12, 2025

Hide Solution

Verified By Collegedunia

The Correct Option is A

The correct answer is(A):

\frac{1}{x^4}

Was this answer helpful?

If $y = y(x)$ is the solution of the differential equation, $\sqrt{4 - x^2} \frac{dy}{dx} = \left( \left( \sin^{-1} \left( \frac{x}{2} \right) \right)^2 - y \right) \sin^{-1} \left( \frac{x}{2} \right),$ where $-2 \leq x \leq 2$ , and $y(2) = \frac{\pi^2 - 8}{4}$ , then $y^2(0)$ is equal to:
- JEE Main - 2025
- Mathematics
- Differential Equations
View Solution
Let $y = y(x)$ be the solution of the differential equation $\left( xy - 5x^2 \sqrt{1 + x^2} \right) dx + (1 + x^2) dy = 0, \quad y(0) = 0.$ Then $y(\sqrt{3})$ is equal to:
- JEE Main - 2025
- Mathematics
- Differential Equations
View Solution
Let a curve $y = f(x)$ pass through the points $(0,5)$ and $(\log 2, k)$ . If the curve satisfies the differential equation: $2(3+y)e^{2x}dx - (7+e^{2x})dy = 0,$ then $k$ is equal to:
- JEE Main - 2025
- Mathematics
- Differential Equations
View Solution
Let $x = x(y)$ be the solution of the differential equation: $y = \left( x - y \frac{dx}{dy} \right) \sin\left( \frac{x}{y} \right), \, y > 0 \, \text{and} \, x(1) = \frac{\pi}{2}.$ Then $\cos(x(2))$ is equal to:
- JEE Main - 2025
- Mathematics
- Differential Equations
View Solution
Let for some function $y = f(x)$ , $\int_0^x t f(t) \, dt = x^2 f(x), x>0$ and $f(2) = 3$ . Then $f(6)$ is equal to:
- JEE Main - 2025
- Mathematics
- Differential Equations
View Solution

View More Questions

View More Questions