Master the Art of Solving Differential Equations!
Welcome to your second worksheet on differential equations! These problems are designed to boost your confidence and understanding. Good luck!
Problem 1: Separation of Variables
Solve the following differential equation: \( \frac{dy}{dx} = xy \)
Problem 2: Homogeneous Equations
Find the general solution of the equation: \( \frac{dy}{dx} = \frac{x^2 + y^2}{xy} \)
Problem 3: Linear Differential Equations
Solve the linear equation \( \frac{dy}{dx} + P(x)y = Q(x) \) for the given functions \( P(x) = x \) and \( Q(x) = x^2 \).