Question

Solve a differential equation x.x.x.dt+cosect.dx=0

Answer 1

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$= > {x}^{3} dt + \cosec(t) dx = 0 \\ \\ = > {x}^{3} dt = - \cosec(t) dx \\ \\ = > \frac{dt}{ \cosec(t) } = - \frac{dx}{ {x}^{3} } \\ \\ = > \sin(t) dt = - {x}^{ - 3} dx \\ \\ = > \int \sin(t) dt = - \int {x}^{ - 3} dx \\ \\ = > - \cos(t) = - \frac{ {x}^{ - 2} }{ - 2} + c \\ \\ = > 2 \cos(t) + \frac{1}{ {x}^{2} } = c$
This is the required general solution
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