Final answer:
To find the general solution of the given equation, rearrange the terms and integrate both sides with respect to x. Then, substitute the boundary conditions into the general solution to find the particular solution of the equation.
Step-by-step explanation:
To find the general solution of the given equation, we can solve for y by rearranging the terms. Start by isolating the dy/dx term on the left side of the equation: x - 2(dy/dx) = -3((x-1)/(x+1))y + 1. Multiply both sides by dx to separate variables: dx/dx - 2(dy/dx)dx = -3((x-1)/(x+1))ydx + dx. Integrating both sides with respect to x, we get: x - 2y = -3∫((x-1)/(x+1))y dx + x + C. Simplifying the integral and combining like terms, we obtain the general solution: x - 2y = -3y(x - 1) + x + C.
To find the particular solution of the equation, we can use the given boundary condition. Substitute the values x = -1 and y = 5 into the general solution: -1 - 2(5) = -3(5(-1 - 1)) + (-1) + C. Simplifying the equation, we can solve for C: -11 = -30 + C. Therefore, C = 19. Substituting this value back into the general solution, we can find the particular solution of the equation: x - 2y = -3y(x - 1) + x + 19.