A differentiable function satisfies dy dx = x+2 x(x-1)
MATHEMATICS · Multi-part · AP · Calculus AB · Differential Equations · Differential Equations
Problem
A differentiable function y=f(x) satisfies
dxdy=x(x−1)x+2,f(2)=0.
Answer the following questions.
(a) Rewrite the differential equation in a form that allows the variables to be separated.
(b) Find an explicit expression for f(x) that satisfies the differential equation.
(c) Use the initial condition to determine the constant of integration.
(d) Evaluate f(3). Show all work and simplify your result.