What is the equation that a curve passes through the origin and the tangent slope at point (x, y) is 2x+y? Advanced mathematics
Let this curve be y=f(x), f(0)=0 (due to crossing the origin), y'=2x+y, that is, y'-y=2x. This is an equation that can be solved by formula method. y = ce x+2x+2 makes x=0 have 0=C+2, so C=-2 is a curve equation.