Show that by making the substitution Show that the solution of this equation is v = 1/2x

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Show that by making the substitution

d.x dt and noting that dx du dt dt the equation dx dt may be expressed as v= du dx d.x -X = || ax=a dt du dx

Show that the solution of this equation is v = 1/2x2 + C and hence find x(t). This technique is a standard method for solving second-order differential equations in which the independent variable does not appear explicitly. Apply the same method to obtain the solutions of the differential equations

(a) (b) (2) dx TIP X-P dt X-P ZIP || || xp -d dt Xp dt = (dr) (x - - ) |2x

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