Question

Solve x {d y}{d x}=3 y-2 x, y(1)=-5

(a) Identify the integrating factor, r(x) .{ r(x)=___ }
(b) Find the general solution. y(x)=_____

Answer 1

To solve the given differential equation, we can use the method of integrating factors.

Step-by-step explanation:

To solve the given differential equation, we can use the method of integrating factors. The integrating factor, r(x), can be found by multiplying the coefficient of y, which is 3, by the differential of x, which is dx. So, r(x) = 3dx.

Using the integrating factor, we can rewrite the equation as (x^3dy - 2xdx) = 3ydx. By rearranging and integrating, we can find the general solution y(x) = (x^3 - 6x^2 + C)/(2x).