Answer to Question #133089 in Differential Equations for Kaye Anne I. Faustino

Question

obtain the differential equation associated with the given primitive, a and b : y = tan (x +a)

Answer 1

The given equation is

y=tan(x+a)

we can write the above equation as

$tan^{-1}y=x+a$

differentiate both sides with respect to x

$\frac{1}{1+y^2}\frac{dy}{dx}=1$

$\frac{dy}{dx}=1+y^2$

$y'-y^2-1=0$