What is the solution for t^2(dx)/(dt)= 1/(x^2),x(4)=9 ?

The solution for t^2(dx)/(dt)= 1/(x^2),x(4)=9 is x=\sqrt[3]{-3/t+2919/4}

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t^2(dx)/(dt)= 1/(x^2),x(4)=9

t^{2} \frac{d x}{d t} = \frac{1}{x ^{2}}, x (4) = 9

x = 3 - \frac{3}{t} + \frac{2919}{4}

Solution steps

t^{2} \frac{d x}{d t} = \frac{1}{x ^{2}}

Solve separable ODE:

x = 3 - \frac{3}{t} + \frac{2919}{4}

x = 3 - \frac{3}{t} + \frac{2919}{4}

\frac{d}{d x} (3 x^{2} + 6 x + cos (x))

y^{^{'}} = tan (x) (sec (x))^{4}

\int x^{3} e^{7 x} d x

y^{^{'}} - 3 y = 6, y (0) = 1

\int e^{a x} x d x

What is the solution for t^2(dx)/(dt)= 1/(x^2),x(4)=9 ?
The solution for t^2(dx)/(dt)= 1/(x^2),x(4)=9 is x=\sqrt[3]{-3/t+2919/4}