Exams › JEE Main › Maths

Find the equation of the curve that satisfies (xy - x²) (dy)/(dx) = y² and passes through the point (-1, 1).

1. y = (log y − 1)x
2. y = (log y + 1)x
3. x = (log x − 1)y
4. x = (log x + 1)y

Correct answer: y = (log y − 1)x

Solution

The correct option is derived from solving the differential equation, which involves separating variables and integrating. The solution satisfies the initial condition given by the point (-1, 1), confirming that it is the appropriate equation for the curve.

Related JEE Main Maths questions

• If √(1-x²ⁿ)+√(1-y²ⁿ)=a(xⁿ-yⁿ), then the value of (√(1-x²ⁿ) dy)/(√(1-y²ⁿ) dx) is
• For a curve that passes through the point (4, 0), the slope is governed by dy/dx = y/x + 5x/((x + 2)(x − 3)). If the point (5, a) lies on this curve, what is the value of a?
• Which differential equation represents the family of all conics whose axes are aligned with the coordinate axes?
• For the differential equation y = y/x + x/y, if its general solution is written as y = x / log|Cx|, then the function φ(x/y) is
• For the differential equation dy/dx = [y f'(x) − y²]/f(x), where f(x) is a specified function, the solution is
• The differential equation sec²x·tan y dx + sec²y·tan x dy = 0 has which general solution?

⚔️ Practice JEE Main Maths free + battle 1v1 →