BCA Semester 2 – Mathematics II – Unit 5: Differential Equations (7Hrs)

Given differential equation: \[ \sin x \frac{dy}{dx} + (\cos x)y = -\sin x \cos x \] --- $\textbf{Step 1: Convert into standard linear form}$ Divide the entire equation by \( \sin x \): \[ \frac{dy}{

Step 1: Rewrite the equation in standard form Divide both sides by 2: \[ \frac{dy}{dx} = \frac{y}{x} + \frac{y^2}{2x^2} \] \[ \frac{dy}{dx} - \frac{y}{x} = \frac{y^2}{2x^2} \] --- Step 2: Recognize a

Step 1: Rewrite in standard linear form \[ \frac{dy}{dx} + \frac{2}{x} y = x \log x \quad (x \neq 0) \] This is a first-order linear differential equation of the form: \[ \frac{dy}{dx} + P(x) y = Q(x)