Exams › JEE Main › Maths
By eliminating the arbitrary constant c, find the differential equation whose general solution is x = c*y*e^(xy).
- dy/dx = y*(1 - xy) / (x*(1 + xy))
- dy/dx = x*(1 - xy) / (y*(1 + xy))
- dy/dx = y*(1 + xy) / (x*(1 - xy))
- dy/dx = (1 - xy) / (1 + xy)
Correct answer: dy/dx = y*(1 - xy) / (x*(1 + xy))
Solution
Taking logs turns x = c*y*e^(xy) into ln(x) = ln(c) + ln(y) + xy. Differentiating eliminates the constant c automatically. The result is rearranged to express dy/dx purely in terms of x and y, giving a first-order differential equation that the original family of curves satisfies.
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?
- Find the equation of the curve that satisfies (xy - x²) (dy)/(dx) = y² and passes through the point (-1, 1).
- 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
⚔️ Practice JEE Main Maths free + battle 1v1 →