Exams › JEE Main › Maths
The differential equation (dy)/(dx)=(y)/(x)+(φ(y/x))/(φ'(y/x)) has which of the following as its solution?
- x φ(y/x)=k
- φ(y/x)=kx
- y φ(y/x)=k
- φ(y/x)=ky
Correct answer: φ(y/x)=kx
Solution
The correct option, ( ext phi(y/x)=kx ext, is derived from the structure of the differential equation, which suggests a relationship between the variables that can be expressed in terms of the function ( ext phi ext. This form maintains the proportionality between ( exty ext and ( extx ext, consistent with the nature of the equation.
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 →