Answer to Question #231183 in Differential Equations for Randal Rodriguez

Question

eliminate the arbitrary constant using any method

12.y\:=\:3Ax^3\:+\:2Bx^2\:+\:4Cx\:−\:D

Answer 1

$y=3Ax^3+2Bx^2+4Cx-D \\\frac{dy}{dx}=9Ax^2+4Bx+4C ...(1) \\\frac{d^2y}{dx^2}=18Ax+4B ...(2) \\\frac{d^3y}{dx^3}=18A ...(3) \\\frac{d^4y}{dx^4}=0$