Why the order of the differential equation log d square y y d x square?
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By the Chain Rule,
ddy(dydx)2=dxdyddx(dydx)2.ddy(dydx)2=dxdyddx(dydx)2.
Now use the fact that dxdy=1dydx.dxdy=1dydx.
Calculate ddx(dydx)2ddx(dydx)2 using the Product Rule. When we put things together, there is some nice cancellation, which undoubtedly means there is a simple conceptual reason.
ddy(dydx)2=dxdyddx(dydx)2.ddy(dydx)2=dxdyddx(dydx)2.
Now use the fact that dxdy=1dydx.dxdy=1dydx.
Calculate ddx(dydx)2ddx(dydx)2 using the Product Rule. When we put things together, there is some nice cancellation, which undoubtedly means there is a simple conceptual reason.
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