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Suppose that x = x (t ) and y = y (t ) and differentiate the following equation with respect to t.
Solution x3 y6 + e1- x - cos (5 y ) = y 2
Thus, just differentiate as normal & add on proper derivative at each step. Note that the first term will be a product rule as both x and y is functions of t.
3x2 x′y6 + 6x3 y5 y′ - x′e1- x + 5 y′ sin (5 y) = 2 yy′
There actually isn't all that much to this problem. As there are two derivatives in the problem we won't be bothering to solve out for one of them.
At this point there doesn't appear be any real purpose for doing this kind of problem,
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It is not the first time that we've looked this topic. We also considered linear independence and linear dependence back while we were looking at second order differential equation
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