dy/dx = F(x, y) will be a homogeneous differential equation for which of the following functions ? (i) F(x, y) = 3x + 2y (ii) F(x, y) = sin(y/x) + log y – log x (iii) F(x, y) = e^(y/x) + 1 (iv) F(x, y) = √(x² + y²) – y

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Definition of Differential Equation, Homogeneous Differential Equations | PadhAiPro

Question

MCQ (Single)Definition of Differential EquationHomogeneous Differential Equations

Find the particular solution of the differential equation given by x² (dy/dx) – xy = x² cos² (y/(2x)), given that when x = 1, y = π/2.

The differential equation dy/dx = F(x, y) will not be a homogeneous differential equation, if F(x, y) is :

Homogeneous Differential Equations

Find the particular solution of the differential equation given by 2xy + y² – 2x² dy/dx = 0; y = 2, when x = 1.

Find the general solution of the differential equation : y dx = (x + 2y²) dy

Solve the following differential equation : x² dy + y(x + y) dx = 0

The order of the following differential equation d³y/dx³ + x(dy/dx)⁵ = 4 log(d⁴y/dx⁴) is :