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Solve`(d^2y)/(dx^2)=((dy)/(dx))^2` |
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Answer» `(d^(2)y)/(dx^(2))=((dy)/(dx))^(2)` or `d/(dx)(dy)/(dx) = ((dy)/(dx))^(2)` or `(d(dy)/(dx))/((dy)/(dx))=(dy)/(dx)dx` or `int ((d(dy)/(dx)))/((dy)/(dx))=intdy` `therefore log(dy)/(dx)=logy+logC_(1)` `therefore (dy)/(dx)=C_(1)y` `therefore (dy)/(y)=C_(1)dx` `therefore int(dy)/(y) = C_(1)intdx` `therefore logy=C_(1)x+k` `therefore y=e^(C_(1)x+k)=C_(2)e^(C_(1)x)` |
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