Solve dy/dx = (y/x):
Ay = x²
By = ln x
Cy = Cx (linear, homogeneous)
Dy = e^x
Answer & Solution
Correct answer: C. y = Cx (linear, homogeneous)
Variable separable: dy/y = dx/x → ln|y| = ln|x| + C → y = Cx. (Family of lines through origin.)
Related questions
Solution of dy/dx = ky (k > 0) representsThe degree of (d²y/dx²)² + (dy/dx)³ + y = 0 isThe order of the differential equation d²y/dx² + 3 dy/dx + 2y = 0 isEuler's method for a DE y' = f(x, y) computes the next value as:A mass on a spring obeys d²x/dt² + ω²x = 0 (SHM). The period of oscillation is:For the second-order LDE y'' − 5y' + 6y = 0, the auxiliary equation m² − 5m + 6 = 0 has roBy Newton's law of cooling, a hot tea cup at 90°C in a room at 25°C cools so that:If a population grows exponentially as dN/dt = 0.1 N (with t in years), the DOUBLING TIME