Question

Find all solutions of the given differential equations and then find the particular solutions for which a point (x,y) is given:

dy/dx = (3x - 4)

Answer 1

$\frac{dy}{dx}=3x-4\\ dy=(3x-4)dx\\ \text{Integrating both side, we get}\\ y=\frac{3}{2}x^2-4x+c\\ \text{This is the general solution. There are infinite solution because c has infinite choices.}\\ \text{To find particular solution we need one initial condition. So that, we get a fixed value of constant c.}$