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Find the general solution of the given differential equation: 2(dy/dx) - 6y = 3.

User Afifa
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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.

  1. First, divide both sides of the equation by (3 + 6y): (1/(3 + 6y))dy/dx = 1/2.
  2. Integrate both sides with respect to x: ∫(1/(3 + 6y))dy = ∫(1/2)dx.
  3. 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.

User Heron Rossi
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