Final answer:
To find the general solution of the given differential equation 2(dy/dx) - 6y = 3, rearrange the equation and solve using the method of integrating factors.
Step-by-step explanation:
To find the general solution of the given differential equation 2(dy/dx) - 6y = 3, we can start by rearranging the equation: dy/dx = (3 + 6y)/2. This is a first-order linear ordinary differential equation, and we can solve it using the method of integrating factors.
- First, divide both sides of the equation by (3 + 6y): (1/(3 + 6y))dy/dx = 1/2.
- Integrate both sides with respect to x: ∫(1/(3 + 6y))dy = ∫(1/2)dx.
- Solve the integrals using appropriate substitution methods to find the general solution of y in terms of x.
The general solution would be in the form of y = f(x), where f(x) is the function obtained after integrating the equation.