Solve the differential equation dy/dx = y/x(x + 1) , given that when x = 1, y = 1. Your answer should express y explicitly in terms of x.
Rearrange differential equation to get 1/x(x+1) dx = 1/y dy. Separate x side into partial fractions where 1/x(x+1) = 1/x - 1/(x+1). Integrate each side. Resulting equation involves natural logs. Substitute in boundary conditions (known values of x and y) to find a value for the integration constant. Simplify the equation on the x side using standard log rules. Raise e to the power of each side of the equation to remove natural logs. Hence, y=2x/(x+1).
AT
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