Separable Equations | MCQs

Explanation

To solve the separable differential equation:

(1 + x)dy - ydx = 0

Rearrange the equation:

(1 + x)dy = ydx

Separate the variables:

dy/y = dx/(1 + x)

Integrate both sides:

∫(dy/y) = ∫(dx/(1 + x))

ln(y) = ln(1 + x) + C

y = e^(ln(1 + x) + C)

= e^C * e^(ln(1 + x))

= c(1 + x)