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2 December, 00:01

What is the general solution to the ODE

/[dy/dx = 2y+1?/]

Use separation of variables.

Is y' + xy = x separable?

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  1. 2 December, 03:13
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    we are given the ordinary differential equation of dy/dx = 2y+1. The ODE is variable separable which means x and y can be grouped altogether explicitly. In this case, the equation becomesdy / 2y + 1 = dx

    1/2 ln (2y + 1) = x + ln Cln (2y + 1) = 2x + ln C2y + 1 = C e 2x y = (C e 2x - 1) / 2

    The ODE y' + xy = x can be grouped into y' + x (y-1) = 0 'y' / y-1 = - xThis is variable separable
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