Show that, by making the substitution y = at + bx + c, equations of the form

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Show that, by making the substitution y = at + bx + c, equations of the form

dx dt = f(at + bx + c)

can be reduced to separable form. Hence find the general solutions of the following differential equations:

(a) (c) (e) 09 | [ dx dt dx dt dx dt dx dt t-x+ 2 t-x+ 3 1 - 2x - t 4x + 2t = 2t + x + 2 (b) 2- (d) 2 dx- dt

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