What is a differential equation

That oondition has been eliminated. Equation (2), therefore, represents a straight line fulfilling one oondition, namely, that it makes an angle tan lm with the rc-axis. Now substitute (2) in (1), the resulting equation, 

Equation (6) tells us not only that the acceleration is constant, but it fixes that value to the definite magnitude g ft. per second. Remembering that acceleration measures the rate of change of velocity, and integrating (6), we get, 

From 71, we have learnt how to find the meaning of Gv Put t = 0, then ds/dt = Gv This means that when we begin to reckon the velocity, the body may have been moving with a definite velocity Cv Let Cj = vQ ft. per second. Of course if the body started from a position of rest, C1 = 0. Now integrate (7) and find the value of CQ in the result, 

It had traversed a distance of s0 ft. To use a sporting phrase, if the body is starting from scratch, sQ =0. 

Equation (7) tells us the two latter facts about the moving body equation (6) only tells us the third fact equation (5) tells us nothing more than that the acceleration is constant. (5), therefore, is true of the motion of any body moving with a uniform acceleration. 

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What is a differential equation (of a certain type no useful general definition can be given) ... 

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