Question

The solution to the differential equation \[ \frac{dy}{dx} = \frac{yf'(x) - y^2}{f(x)} \] where \( f(x) \) is a given function is

• A. \( f(x) = x + c \)
• B. \( f(x) = cx + y \)
• C. \( f(x) = cx + y \)
• D. \( yf(x) = cx \)

Hint:

When solving first-order differential equations, use separation of variables to isolate \( f(x) \) and solve for it.

Answer 1

The Correct Option is A

Step 1: Separate the variables.
Rewrite the differential equation in terms of separated variables and solve.
Step 2: Solve the equation.
The solution is \( f(x) = x + c \), where \( c \) is a constant. Final Answer: \[ \boxed{f(x) = x + c} \]