Solution of the separable differential equation (1+ x)dy - ydx = 0 is _____?
Solution of the separable differential equation (1+ x)dy - ydx = 0 is _____?
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)