What is the solution for (dx)/(dt)=-t/x ?

The solution for (dx)/(dt)=-t/x is x=sqrt(-t^2+c_{1)},x=-sqrt(-t^2+c_{1)}

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(dx)/(dt)=-t/x

\frac{d x}{d t} = - \frac{t}{x}

x = - t^{2} + c_{1}, x = - - t^{2} + c_{1}

Solution steps

\frac{d x}{d t} = - \frac{t}{x}

Solve separable ODE:

x = - t^{2} + c_{1}, x = - - t^{2} + c_{1}

x = - t^{2} + c_{1}, x = - - t^{2} + c_{1}

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What is the solution for (dx)/(dt)=-t/x ?
The solution for (dx)/(dt)=-t/x is x=sqrt(-t^2+c_{1)},x=-sqrt(-t^2+c_{1)}